Definite Integrals Questions and Answers
![2 Find the volume of the solid region bounded by the graphs of the equations z 9 x y 3x y 3 x 0 y 0 z 0](https://media.kunduz.com/media/sug-question-candidate/20221214151902750909-5078300.jpg?w=256)
Calculus
Definite Integrals2 Find the volume of the solid region bounded by the graphs of the equations z 9 x y 3x y 3 x 0 y 0 z 0
![xample 1 1 Sex dx Use the CSR Asw with n 8 to approximate 113 0 0315](https://media.kunduz.com/media/sug-question-candidate/20221214105450499327-3494185.jpg?w=256)
![2 Given f x 4x 5 and g x x 5 write an equation for g f x g f x 4 x 5 5 g f x 2 x a a 3 Let f x 10x 1 Write an expression for f x 2 f x C C 10 8 b d 2 20 b d](https://media.kunduz.com/media/sug-question-candidate/20221214025126584764-5184814.jpg?w=256)
Calculus
Definite Integrals2 Given f x 4x 5 and g x x 5 write an equation for g f x g f x 4 x 5 5 g f x 2 x a a 3 Let f x 10x 1 Write an expression for f x 2 f x C C 10 8 b d 2 20 b d
![Use the piecewise function to evaluate the following H a f 4 a c f 3 e f 0 b f 1 d f 2](https://media.kunduz.com/media/sug-question-candidate/20221213222338066921-4338747.jpg?w=256)
Calculus
Definite IntegralsUse the piecewise function to evaluate the following H a f 4 a c f 3 e f 0 b f 1 d f 2
![Evaluate the line integral 0 3 0 2 03 2 01 02 2 3yzds where Cis the curve with parametric equations 2 t y sint z cost 0](https://media.kunduz.com/media/sug-question-candidate/20221213170205273162-5133347.jpg?w=256)
Calculus
Definite IntegralsEvaluate the line integral 0 3 0 2 03 2 01 02 2 3yzds where Cis the curve with parametric equations 2 t y sint z cost 0
![5 4 3 2 4 3 2 1 y 2 3 4 5 12 3 4 5 Find the inequality represented by the graph I](https://media.kunduz.com/media/sug-question-candidate/20221213160845813643-5006639.jpg?w=256)
Calculus
Definite Integrals5 4 3 2 4 3 2 1 y 2 3 4 5 12 3 4 5 Find the inequality represented by the graph I
![Evaluate the line integral PF dr by evaluating the surface integral in Stokes Theorem with an appropriate choice of S Assume that C has a counterclockwise orientation when C F 5y z x C is the circle x y 22 in the plane z 0 Rewrite the given line integral as an area integral over the appropriate region of the xy plane SS 5 da dA R C dr Evaluate the integral Er Type an exact answer COLOS](https://media.kunduz.com/media/sug-question-candidate/20221212203727607220-4345941.jpg?w=256)
Calculus
Definite IntegralsEvaluate the line integral PF dr by evaluating the surface integral in Stokes Theorem with an appropriate choice of S Assume that C has a counterclockwise orientation when C F 5y z x C is the circle x y 22 in the plane z 0 Rewrite the given line integral as an area integral over the appropriate region of the xy plane SS 5 da dA R C dr Evaluate the integral Er Type an exact answer COLOS
![Evaluate the surface integral f x y z ds using an explicit representation of the surface S f x y z 4xy S is the plane z 1 x y in the first octant Set up the surface integral for the given function f x y z over the given surface S Integrate with respect to x first Use increasing limits of integra 00 S S O dx dy 00 SS f x y z ds S Type exact answers](https://media.kunduz.com/media/sug-question-candidate/20221212170757834647-4345941.jpg?w=256)
Calculus
Definite IntegralsEvaluate the surface integral f x y z ds using an explicit representation of the surface S f x y z 4xy S is the plane z 1 x y in the first octant Set up the surface integral for the given function f x y z over the given surface S Integrate with respect to x first Use increasing limits of integra 00 S S O dx dy 00 SS f x y z ds S Type exact answers
![Select the equivalent expression 1 3 p 12](https://media.kunduz.com/media/sug-question-candidate/20221212174010404655-5169704.jpg?w=256)
![Find the area of the surface of the half cylinder r 0 z r 3 0 0sx 0 zs 7 using a parametric description of the surface Set up the integral for the surface area using the parameterization u 0 and v z SSO 00 Type an exact answers using a as needed du dv](https://media.kunduz.com/media/sug-question-candidate/20221212170632166168-4345941.jpg?w=256)
Calculus
Definite IntegralsFind the area of the surface of the half cylinder r 0 z r 3 0 0sx 0 zs 7 using a parametric description of the surface Set up the integral for the surface area using the parameterization u 0 and v z SSO 00 Type an exact answers using a as needed du dv
![and the area of the following surface using the given explicit description of the surface z 3 x y2 for 0 sz 108 The paraboloid z Set up the surface integral for the given function over the given surface S as a double integral over a region R in the xy plane SS as SSO S R Tyne an exact answer using as needed dA](https://media.kunduz.com/media/sug-question-candidate/20221212170733915880-4345941.jpg?w=256)
Calculus
Definite Integralsand the area of the following surface using the given explicit description of the surface z 3 x y2 for 0 sz 108 The paraboloid z Set up the surface integral for the given function over the given surface S as a double integral over a region R in the xy plane SS as SSO S R Tyne an exact answer using as needed dA
![Use the Binomial Theorem to expand and simplify the expression y 9 4](https://media.kunduz.com/media/sug-question-candidate/20221212170158135633-3899453.jpg?w=256)
![11 Find t e 3x dx a c diverges 0 b d](https://media.kunduz.com/media/sug-question-candidate/20221212163820128824-4709559.jpg?w=256)
![18 The region between the curve y x 0 x 4 and the x axis is revolved about the x axis to generate a solid Find its volume a c 2TT 47 b d 8T 67](https://media.kunduz.com/media/sug-question-candidate/20221212154728335255-4709559.jpg?w=256)
Calculus
Definite Integrals18 The region between the curve y x 0 x 4 and the x axis is revolved about the x axis to generate a solid Find its volume a c 2TT 47 b d 8T 67
![9 5 points Use the limit process to find the area of the region bounded by the graph of the function and the x axis over the given interval y 5 r 2 1 Sketch the region](https://media.kunduz.com/media/sug-question-candidate/20221212141354956089-4536393.jpg?w=256)
Calculus
Definite Integrals9 5 points Use the limit process to find the area of the region bounded by the graph of the function and the x axis over the given interval y 5 r 2 1 Sketch the region
![Evaluate the definite integral f2r x 1 dx](https://media.kunduz.com/media/sug-question-candidate/20221212141623112228-4536393.jpg?w=256)
![4 Find the area of the region enclosed by r 2 cos 0 a b 7 4 c 4 9 2 FORT HUBERT S d 5T](https://media.kunduz.com/media/sug-question-candidate/20221212135045158084-4709559.jpg?w=256)
Calculus
Definite Integrals4 Find the area of the region enclosed by r 2 cos 0 a b 7 4 c 4 9 2 FORT HUBERT S d 5T
![Let R be the region in the xy plane bounded between y 4 x and y 1 x Set up an integral that is equal to the volume of the solid obtained by revolving R about the line x 5 using a the cylindrical shell method and b the washer method Do not evaluate the integral s](https://media.kunduz.com/media/sug-question-candidate/20221212074641839247-3636182.jpg?w=256)
Calculus
Definite IntegralsLet R be the region in the xy plane bounded between y 4 x and y 1 x Set up an integral that is equal to the volume of the solid obtained by revolving R about the line x 5 using a the cylindrical shell method and b the washer method Do not evaluate the integral s
![As blood moves through a vein or an artery its velocity v is greatest along the central axis and decreases as the function of r is called the law of laminar flow For an artery with radius 0 5 cm the relationship between v in cm s and r in cm is given by the function v r 18 500 0 25 2 Osrs0 5 0 5 cm a Find v 0 1 and v 0 4 v 0 1 4440 v 0 4 16650 cm s x cm s b What do your answers to part a tell you about the flow of blood in this artery The blood flows much faster 0 1 cm from the center than 0 1 cm from the edge The blood flows much slower 0 1 cm from the center than 0 1 cm from the edge The blood flows with the same velocity 0 1 cm from the center as it does 0 1 cm from the edge Nothing can be determined about blood flow from part a c Make a table of values of v r for r 0 0 1 0 2 0 3 0 4 0 5 r in cm V r in cm s 0 4625 0 1 4440 0 2 3885 0 3 2960 0 4 1665 0 5 0](https://media.kunduz.com/media/sug-question-candidate/20221212042854299334-4838748.jpg?w=256)
Calculus
Definite IntegralsAs blood moves through a vein or an artery its velocity v is greatest along the central axis and decreases as the function of r is called the law of laminar flow For an artery with radius 0 5 cm the relationship between v in cm s and r in cm is given by the function v r 18 500 0 25 2 Osrs0 5 0 5 cm a Find v 0 1 and v 0 4 v 0 1 4440 v 0 4 16650 cm s x cm s b What do your answers to part a tell you about the flow of blood in this artery The blood flows much faster 0 1 cm from the center than 0 1 cm from the edge The blood flows much slower 0 1 cm from the center than 0 1 cm from the edge The blood flows with the same velocity 0 1 cm from the center as it does 0 1 cm from the edge Nothing can be determined about blood flow from part a c Make a table of values of v r for r 0 0 1 0 2 0 3 0 4 0 5 r in cm V r in cm s 0 4625 0 1 4440 0 2 3885 0 3 2960 0 4 1665 0 5 0
![27 Find a formula for the nth term of the arithmetic sequence 6 2 2 6 10 OA 6 4n B 6 2n O C 10 2n D 10 4n](https://media.kunduz.com/media/sug-question-candidate/20221212041136782803-4107770.jpg?w=256)
Calculus
Definite Integrals27 Find a formula for the nth term of the arithmetic sequence 6 2 2 6 10 OA 6 4n B 6 2n O C 10 2n D 10 4n
![The formula A 21 20 0409 a What was the population of the state in 2000 b When will the population of the state reach 29 8 million models the population of a US state A in millions t years after 200](https://media.kunduz.com/media/sug-question-candidate/20221211201242810140-5174752.jpg?w=256)
Calculus
Definite IntegralsThe formula A 21 20 0409 a What was the population of the state in 2000 b When will the population of the state reach 29 8 million models the population of a US state A in millions t years after 200
![4 Find P a da P x dx for k 2 3 4 5 and 6](https://media.kunduz.com/media/sug-question-candidate/20221211045813500649-5133347.jpg?w=256)
![6 10 pts Use Stokes Theorem to evaluate the integral f F dr where x y z ayi z2j 3y2 k and C is the trace of the cylinder z y2 9 in the plane 2r 8 oriented counterclockwise as viewed from above](https://media.kunduz.com/media/sug-question-candidate/20221210180016740455-5133347.jpg?w=256)
Calculus
Definite Integrals6 10 pts Use Stokes Theorem to evaluate the integral f F dr where x y z ayi z2j 3y2 k and C is the trace of the cylinder z y2 9 in the plane 2r 8 oriented counterclockwise as viewed from above
![c Consider the solid in the first octant cut off from the square cylinder with sides x 0 x 1 y 0 and y 1 by the plane x y z 4 Find the volume 3 ways i A da dz dy integration 15 points ii A dz dy dx integration 15 points](https://media.kunduz.com/media/sug-question-candidate/20221210091158347073-5165346.jpg?w=256)
Calculus
Definite Integralsc Consider the solid in the first octant cut off from the square cylinder with sides x 0 x 1 y 0 and y 1 by the plane x y z 4 Find the volume 3 ways i A da dz dy integration 15 points ii A dz dy dx integration 15 points
![Use the surface integral in Stokes Theorem to calculate the flux of the curl of the field F across the surface S in the direction away from the origin F 4yi 5 5x j z 2 k S r 0 2 sin cos 0 i 2 sin osin 0 j 2 cos 4 k 0 r 2 0 0 2](https://media.kunduz.com/media/sug-question-candidate/20221209233917185118-5132744.jpg?w=256)
Calculus
Definite IntegralsUse the surface integral in Stokes Theorem to calculate the flux of the curl of the field F across the surface S in the direction away from the origin F 4yi 5 5x j z 2 k S r 0 2 sin cos 0 i 2 sin osin 0 j 2 cos 4 k 0 r 2 0 0 2
![Find the domain of f and write your answer in interval notation f x 2x 9 x 12x 32](https://media.kunduz.com/media/sug-question-candidate/20221210001805977922-4920292.jpg?w=256)
Calculus
Definite IntegralsFind the domain of f and write your answer in interval notation f x 2x 9 x 12x 32
![What is the third term in the binomial expansion of 3x y 4 O 54x O 18x y3 O 18x 6 O 54x y6](https://media.kunduz.com/media/sug-question-candidate/20221209220031721228-4394539.jpg?w=256)
Calculus
Definite IntegralsWhat is the third term in the binomial expansion of 3x y 4 O 54x O 18x y3 O 18x 6 O 54x y6
![The region R in the first quadrant is bounded by the graph of y = tan(x), the x-axis, and the vertical line x = 1. What is the volume of the solid formed by revolving R around the vertical line x = 1? 0.3751 0.7012 1.1783 2.203](https://media.kunduz.com/media/sug-question/raw/78303619-1660505873.9483776.jpeg?w=256)
Calculus
Definite IntegralsThe region R in the first quadrant is bounded by the graph of y = tan(x), the x-axis, and the vertical line x = 1. What is the volume of the solid formed by revolving R around the vertical line x = 1? 0.3751 0.7012 1.1783 2.203
![For the polynomial function below, answer parts (a) through (d).
(a) List each real zero and its multiplicity. (b) Determine whether the graph crosses or touches the x-axis at each x-intercept. (c) Determine the maximum number of turning points on the graph. (d) Determine the end
behavior; that is, find the power function that the graph of f resembles for large values of |x|.
f(x)=8(x² +9) (x²+8) ²
GLITOR
(a) Find any real zeros of f. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
OA. The real zero(s) of f is/are
(Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
B. There are no real zeros.](https://media.kunduz.com/media/sug-question/raw/78110447-1660421410.3021095.jpeg?w=256)
Calculus
Definite IntegralsFor the polynomial function below, answer parts (a) through (d).
(a) List each real zero and its multiplicity. (b) Determine whether the graph crosses or touches the x-axis at each x-intercept. (c) Determine the maximum number of turning points on the graph. (d) Determine the end
behavior; that is, find the power function that the graph of f resembles for large values of |x|.
f(x)=8(x² +9) (x²+8) ²
GLITOR
(a) Find any real zeros of f. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
OA. The real zero(s) of f is/are
(Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
B. There are no real zeros.
![1. Evaluate the iterated integral:
3 √9-x^2
∫ ∫ (x² + y²)dy dx
0 -√9-x^2](https://media.kunduz.com/media/sug-question/raw/85025793-1660411876.634946.jpeg?w=256)
![Evaluate the definite integral
S 8 sin(x)dz](https://media.kunduz.com/media/sug-question/raw/84155743-1660408533.432735.jpeg?w=256)
![Let f(x, y) = x sin(x² + y) +x+y for z, y € (-00, 00). Which of the following statement
is true?
(a)
9²
(b) f(x, y)dy = -x cos(z² + a) + x cos(x²) + ax + for a > 0.
2
f(x,y)
lim
(2,3)+(0,0) x(x² + y) = 1.
(c)f(x, y) = 2x² cos(x² + y) + sin(x² + y) + 1.
(d) The tagent planc to the surface z = f(x, y) at the point (0,0,0) is z = 2x + y.
(e) None of the above statements is truc.](https://media.kunduz.com/media/sug-question/raw/84150376-1660408509.2072673.jpeg?w=256)
Calculus
Definite IntegralsLet f(x, y) = x sin(x² + y) +x+y for z, y € (-00, 00). Which of the following statement
is true?
(a)
9²
(b) f(x, y)dy = -x cos(z² + a) + x cos(x²) + ax + for a > 0.
2
f(x,y)
lim
(2,3)+(0,0) x(x² + y) = 1.
(c)f(x, y) = 2x² cos(x² + y) + sin(x² + y) + 1.
(d) The tagent planc to the surface z = f(x, y) at the point (0,0,0) is z = 2x + y.
(e) None of the above statements is truc.
![If
["* f(z)dz = [ f(z)dz + ["* f(z)dz –
-
2
what are the bounds of integration for the first integral?
0=
and
b=
e-,f(t)dt,](https://media.kunduz.com/media/sug-question/raw/84140138-1660407150.3788288.jpeg?w=256)
Calculus
Definite IntegralsIf
["* f(z)dz = [ f(z)dz + ["* f(z)dz –
-
2
what are the bounds of integration for the first integral?
0=
and
b=
e-,f(t)dt,
![If 5 is the hemisphere a² + y² +2²= 25 with z>0 then the surface integal
f(x-2y)ds is__](https://media.kunduz.com/media/sug-question/raw/84116214-1660405647.8185012.jpeg?w=256)
Calculus
Definite IntegralsIf 5 is the hemisphere a² + y² +2²= 25 with z>0 then the surface integal
f(x-2y)ds is__
![How many significant figures are in the number 21.2?
21.2 has [?] significant figures.](https://media.kunduz.com/media/sug-question/raw/84112717-1660404598.505773.jpeg?w=256)
Calculus
Definite IntegralsHow many significant figures are in the number 21.2?
21.2 has [?] significant figures.
![Solve the following system of equations (use any method):
2x-5y=11
-3x+4y=-13
O (-2,-3)
O (3.-1)
O(-3.1)](https://media.kunduz.com/media/sug-question/raw/84081870-1660403877.5054965.jpeg?w=256)
Calculus
Definite IntegralsSolve the following system of equations (use any method):
2x-5y=11
-3x+4y=-13
O (-2,-3)
O (3.-1)
O(-3.1)
![The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method.
x = (y - 6)², x = 25; about y = 1](https://media.kunduz.com/media/sug-question/raw/85021797-1660379971.572283.jpeg?w=256)
Calculus
Definite IntegralsThe region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method.
x = (y - 6)², x = 25; about y = 1
![Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified axis.
x = 4y², y ≥ 0, x = 4; about y = 2](https://media.kunduz.com/media/sug-question/raw/85021795-1660379953.4613547.jpeg?w=256)
Calculus
Definite IntegralsUse the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified axis.
x = 4y², y ≥ 0, x = 4; about y = 2
![Apply Laplace transform method improper integral from 0 to infinity
∫e^-3t sint cost dt](https://media.kunduz.com/media/sug-question/raw/83598919-1660327359.418632.jpeg?w=256)
Calculus
Definite IntegralsApply Laplace transform method improper integral from 0 to infinity
∫e^-3t sint cost dt
![What is the amplitude of the
following function?
y = 0.918 cos x](https://media.kunduz.com/media/sug-question/raw/84079900-1660326549.5837233.jpeg?w=256)
![(0.00/1.00 point)
Use a system of linear equations with two variables and two equations to solve. A concert manager counted 350 ticket receipts the day after
a concert. The price for a student ticket was $12.50, and the price for an adult ticket was $16.00. The register confirms that $5,075 was taken
in. How many student tickets and adult tickets were sold? Let a represent the total number of student tickets sold, and let y represent the
total number of adult tickets sold. Give you answer as an ordered pair (x, y).](https://media.kunduz.com/media/sug-question/raw/84003830-1660325829.034016.jpeg?w=256)
Calculus
Definite Integrals(0.00/1.00 point)
Use a system of linear equations with two variables and two equations to solve. A concert manager counted 350 ticket receipts the day after
a concert. The price for a student ticket was $12.50, and the price for an adult ticket was $16.00. The register confirms that $5,075 was taken
in. How many student tickets and adult tickets were sold? Let a represent the total number of student tickets sold, and let y represent the
total number of adult tickets sold. Give you answer as an ordered pair (x, y).
![Solve the equation by applying the square root property. If there is more than one
solution, enter them in order from smallest to largest. Be sure to write a set as the
answer. Do not enter any spaces in the answer.
(x + 5)² = 9
The solution set is
A/](https://media.kunduz.com/media/sug-question/raw/83749069-1660322115.6488738.jpeg?w=256)
Calculus
Definite IntegralsSolve the equation by applying the square root property. If there is more than one
solution, enter them in order from smallest to largest. Be sure to write a set as the
answer. Do not enter any spaces in the answer.
(x + 5)² = 9
The solution set is
A/
![Solve the equation, then select all true statements about the equation.
4(x-7)= 4x - 28
a) The solution set is the empty set.
b) The equation is a conditional equation.
c) The solution set is {0}.
d) The solution set is the set of all real numbers.
e) The equation is a contradiction.
ntion is an identity.](https://media.kunduz.com/media/sug-question/raw/83748992-1660321253.0440648.jpeg?w=256)
Calculus
Definite IntegralsSolve the equation, then select all true statements about the equation.
4(x-7)= 4x - 28
a) The solution set is the empty set.
b) The equation is a conditional equation.
c) The solution set is {0}.
d) The solution set is the set of all real numbers.
e) The equation is a contradiction.
ntion is an identity.
![9. Use the washer method to the find the volume of the solid of revolution formed by
revolving the region between y = r² and y = √ around the z-axis. Set the two functions
equal to each other to determine the limits of integration. Draw a sketch to determine the
upper and lower functions.](https://media.kunduz.com/media/sug-question/raw/83555773-1660319580.163951.jpeg?w=256)
Calculus
Definite Integrals9. Use the washer method to the find the volume of the solid of revolution formed by
revolving the region between y = r² and y = √ around the z-axis. Set the two functions
equal to each other to determine the limits of integration. Draw a sketch to determine the
upper and lower functions.
![Determine the volume of the solid generated by rotating function f(z) =
[4,10].
100
-z² about the x-axis on
-](https://media.kunduz.com/media/sug-question/raw/85017570-1660319322.2540145.jpeg?w=256)
Calculus
Definite IntegralsDetermine the volume of the solid generated by rotating function f(z) =
[4,10].
100
-z² about the x-axis on
-
![Givenc (x is number of items)
Demand function: (z)
Supply function: a(z)=2./2
Find the equilibrium quantity:
2200
Find the consumers surplus at the equilibrium quantity: 9](https://media.kunduz.com/media/sug-question/raw/85017602-1660319315.1872578.jpeg?w=256)
Calculus
Definite IntegralsGivenc (x is number of items)
Demand function: (z)
Supply function: a(z)=2./2
Find the equilibrium quantity:
2200
Find the consumers surplus at the equilibrium quantity: 9
![=
Sketch the region enclosed by y = 7x and y
6x2. Find the area of the region.](https://media.kunduz.com/media/sug-question/raw/85017565-1660319299.0263488.jpeg?w=256)
Calculus
Definite Integrals=
Sketch the region enclosed by y = 7x and y
6x2. Find the area of the region.
![18
A company's marginal cost function is
where x is the number of units.
Find the total cost of the first 49 units (of increasing production from x=0 to x=49)
Total cost: S](https://media.kunduz.com/media/sug-question/raw/85015388-1660319279.6849682.jpeg?w=256)
Calculus
Definite Integrals18
A company's marginal cost function is
where x is the number of units.
Find the total cost of the first 49 units (of increasing production from x=0 to x=49)
Total cost: S
![10. Use the washer method to the find the volume of the solid of revolution formed by
revolving the region between y = 1 and y = r around the r-axis. Set the two functions.
equal to each other to determine the limits of integration. Draw a sketch to determine the
upper and lower functions.](https://media.kunduz.com/media/sug-question/raw/83558464-1660316136.9856029.jpeg?w=256)
Calculus
Definite Integrals10. Use the washer method to the find the volume of the solid of revolution formed by
revolving the region between y = 1 and y = r around the r-axis. Set the two functions.
equal to each other to determine the limits of integration. Draw a sketch to determine the
upper and lower functions.
![A curve has equation y = f(x).
(a) Write an expression for the slope of the secant line through the points P(7, f(7)) and Q(x, f(x)).
f(x) - x
f(7)-7
O
O X-7
f(x)-f(7)
Of(x)-f(7)
x-7
O
f(7) -7
f(x)
X
(b) Write an expression for the slope of the tangent line at P.
f(x)-f(7)
X-7
O lim
x-0
X-7
x-7 f(x)-f(7)
Olim
Olim
f(x) = f(7)
x-7
f(x) - x
x-0 (7)-7
Olim](https://media.kunduz.com/media/sug-question/raw/83597688-1660315755.0608041.jpeg?w=256)
Calculus
Definite IntegralsA curve has equation y = f(x).
(a) Write an expression for the slope of the secant line through the points P(7, f(7)) and Q(x, f(x)).
f(x) - x
f(7)-7
O
O X-7
f(x)-f(7)
Of(x)-f(7)
x-7
O
f(7) -7
f(x)
X
(b) Write an expression for the slope of the tangent line at P.
f(x)-f(7)
X-7
O lim
x-0
X-7
x-7 f(x)-f(7)
Olim
Olim
f(x) = f(7)
x-7
f(x) - x
x-0 (7)-7
Olim