# Calculus Questions

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Application of derivatives
Perform long division on the integrand write the proper fraction as a sum of partial fractions and then evaluate the integral 12x 24x 1 2x 12x 12x 24x 1 2x dx dx Calculus
Application of derivatives
Express the integrand as a sum of partial fractions and evaluate the integral 12 y S 6 Y 2y 3 dy Express the integrand as a sum of partial fractions y 2y 3 Simplify your answer Use integers or fractions for any numbers in the expression Calculus
Limits & Continuity
The accompanying data represent the percentages of teenagers in various countries that have used certain drugs Complete parts a through c below J K D B C D 40 5 20 1 E F G 37 19 22 16 H 1 5 6 4 52 35 3 17 7 14 4 31 23 Country Drug 1 x Other Drugs y A 22 5 a Determine the correlation coefficient between the percentage of teenagers who have used Drug 1 and the percentage who have used other drugs r Round to two decimal places as needed b Find the equation of the regression line for the percentage of teenagers who have used Drug 1 and the percentage who have used other drugs y x Round to two decimal places as needed c What percentage of teenagers can be anticipated to use drugs other than Drug 1 in a country where 10 of teenagers have used Drug 1 Round to the nearest whole number as needed Calculus
Application of derivatives
and 12 6 5 section Is the given ordered pair a solution to the system 6 4 3x y 22 2x 3y 24 O Yes No Calculus
Application of derivatives
Score 7 86 12 9 12 answered Question 11 Below one description one graph and one equation are equivalent Choose the proper set 10 9 8 7 You start with 3 Xbox360 games and each month you buy 2 new games You start with 1 Xbox360 games and each month you buy 3 new games Oy 3x 1 Oy 2x 3 do 10 9 8 7 5 2 3 4 6 7 8 9 p Calculus
Vector Calculus
Question 8 Terry is skiing down a steep hill Terry s elevation E t in feet after t seconds is given by E t 3700 40t The equation tells us that Terry started Select an answer Select an answer and his Select an answer is Select an answer by Select an answer Question Help Moc Calculus
Vector Calculus
Score 3 12 3 12 answered Question 9 If f x is a linear function f 5 5 and f 2 f x Question Help Video Message instructor 1 4 find an equation for f x Calculus
Application of derivatives
Question 10 A clothing business finds there is a linear relationship between the number of shirts n it can sell and the price p it can charge per shirt In particular historical data shows that 3000 shirts can be sold at a price of 35 while 10000 shirts can be sold at a price of 14 Give a linear equation in the form p mn b that gives the price p they can charge for n shirts Answer p Round the value of your slope to three decimal places Be careful to use the proper variable and use the Preview button to check your syntax before you submit your answer Question Help Video Message instructor Submit Question Calculus
Application of derivatives
Question 9 2 2 19 Part 1 of 6 Find the exact values of the six trigonometic functions for the following angle 45 HW O sin 45 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationalize all dem Calculus
Vector Calculus
B 50 Need Help Submit Answer 0 06 0 12 Points X T X Read it Watch It DETAILS MY NOTES ASK YOUR TEACHER A graphing calculator is recommended Let f x 4e cos x a Find f x and f x PREVIOUS ANSWERS SCALCET9 3 3 034 PRACTICE ANOTHER Calculus
Application of derivatives
Differentiate y 8x 5 tan x Calculus
Application of derivatives
A ladder 20 ft long rests against a vertical wall Let be the angle between the top of the ladder and the wall and let x be the distance from the bottom of the ladder to the wall If the bottom of the ladder slides away from the wall how fast in ft rad doe x change with respect to when 8 ft rad 2 3 Calculus
Definite Integrals
f x COS X f x sin x cot 4 d cot x cos ec x Enhanced Feedback Please try again using the rules for differentiating trigonometric functions Keep in mind that sin x cos x and dx cot x csc x Calculus
Differentiation
A mass on a spring vibrates horizontally on a smooth level surface as shown in the figure Its equation of motion is x c 8 sin t where t is measured in seconds and x In centimeters Equilibrium position t x a Find the velocity and acceleration at time t v t X In what direction is the mass moving at that time O b Find the position velocity and acceleration of the mass at time t 2 3 Calculus
Differentiation
A graphing calculator is recommended Let f x 4e cos x a Find f x and f x f x b Check to see that your answers to part a are reasonable by graphing f f and f y y y y 150 125 100 75 50 25 R N K K X x 7 2 25 50 75 100 100 100 100 125 125 125 125 150 150 DO 150 KIN Describe the relationship between the three graphs Note that f 0 where f has a relative minimum or maximum and f 0 where f has a relative minimum or maximum Also note that f is negative when fis decreasing and f is negative when f is decreasing O Note that f 0 where f has a relative minimum or maximum and f 0 where f has a relative minimum or maximum Also note that f is negative when fis decreasing and f is negative when f is decreasing O Note that f 0 where f has a minimum and f 0 where f has a minimum Also note that f is positive when fis decreasing and f is positive when f is decreasing Note that f 0 where f has a relative minimum or maximum and f 0 where f has a relative minimum or maximum Also note that f is negative when fis decreasing and f is positive when f is decreasing Note that f 0 where f has a maximum and f 0 where f has a maximum Also note that f is positive when f is decreasin Calculus
Differential equations
13 1 0 12 Points Find constants A and B such that the function y A sin x B cos x satisfies the differential equation y y 5y sin x A B Need Help Read It Watch It Calculus
Application of derivatives Calculus
Application of derivatives
5 0 12 Points 7 3 Suppose f a g b h K M 3 F 3 4 and f 7 Let g x f x sin x and h x cos x Find the following f x Calculus
Differentiation
Let the function f be defined by tan x 1 sec x a Use the Quotient Rule to differentiate the function f x f x f x b Simplify the expression for f x by writing it in terms of sin x and cos x and then find f x f x c Show that your answers to parts a and b are equivalent Yes O No Need Help Submit Answer 10 13 Deinal Read It Watch It Calculus
Application of derivatives
Consider the following figure Find lim S 8 0 d Need Help Submit Answer Disc There is a circular arc of length s and a chord of length d both subtended by a central angle 8 18 0 17 Points d 0 S Read It Watch It DETAILS SCALCET9 3 XP 3 002 Calculus
Indefinite Integration
Use an appropriate substitution and then a trigonometric substitution to evaluate the integral In 4 S In 4 et dt 2 81 2t etdt S e2t 81 0 Type an exact answer using radicals as needed Calculus
Indefinite Integration
Use any method to evaluate the integral 30 dx S 225x 1 30 dx 225x 1 S 0 Calculus
Indefinite Integration
Evaluate the integral 169 t dt 169 1 dt Type an exact answer using radicals as needed Calculus
Definite Integrals
Use an appropriate substitution and then a trigonometric substitution to evaluate the integral In 3 S 0 In 3 S 0 e dt 2t 4 e dt 2t ve 4 11 Calculus
Application of derivatives
Evaluate the integral 2 81 y 81 2 dy y 9 Calculus
Indefinite Integration
Use any method to evaluate the following integral 2 S 0 2 S 3dx 3 16 x 3dx 3 2 II 16 x Type an exact answer using radicals as needed Calculus
Indefinite Integration
Evaluate the integral 16 12 dt 16 F dt dt Type an exact answer using radicals as needed Calculus
Indefinite Integration
Use any method to evaluate the integral x dx 3 x dx 3 2 2 x 49 X 49 Calculus
Differentiation
Evaluate the following integral 7 3 2 S 0 49 x2 7 3 2 S 0 T dx dx 49 x Calculus
Application of derivatives
Evaluate 8 3 3 S 8 3 3 dx 64 x 8 3 3 dx 2 64 x 8 3 3 Type an exact answer using and radicals as ne Calculus
Indefinite Integration
Use any method to evaluate the integral x dx 3 S x 2 S x 16 x dx X x 16 2 Calculus
Limits & Continuity
fis the function defined by f x A B C lim x 2 x 2 z 2 lim x 2 lim 2 x 2 2 lim z 2 2 4 24 2 2 then limf x is equivalent to which of the following z 2 Calculus
Limits & Continuity
Use the graph of the function to answer parts a through f P x x 5 1 IN The coordinates of the vertex are 5 1 Type an ordered pair b Give the domain and range What is the domain of P x 0 00 Type your answer in interval notation What is the range of P x 1 00 Type your answer in interval notation c Give the equation of the axis of symmetry x 5 Type an equation d Give the largest open interval over which the function is increasing Type your answer in interval notation 10 B Calculus
Application of derivatives
K Use the graph of the function to answer parts a through f P x 4 x 5 1 a Give the coordinates of the vertex The coordinates of the vertex are 5 1 Type an ordered pair b Give the domain and range What is the domain of P x 0 00 Type your answer in interval notation What is the range of P x 0 1 Type your answer in interval notation c Give the equation of the axis of symmetry Type an equation 10 12 Calculus
Differentiation
Answer the following True False quiz Enter T or F 1 1 g 1 x g x 2 If f c 0 then f has either a local maximum or a local minimum at c 3 Continuous functions are differentiable 4 If f c 0 and f c 0 then f x has a local minimum at c 5 A continuous function on a closed interval a b attains a maximum and a minimum value in a b 6 If f x and g x are increasing on an interval I then f x g r is increasing on I 7 If f x e then f x 2e Calculus
Application of derivatives
f x 9 5e A List all critical numbers of f If there are no critical numbers enter NONE Critical numbers B Use interval notation to indicate where f x is increasing Increasing C List the x coordinates of all local maxima of f If there are no local maxima enter NONE I values of local maxima D Find the x coordinates of all local minima of f If there are no local minima enter NONE I values of local minima E Use interval notation to indicate where f x is concave down Concave down F List the values of all inflection points of f If there are no inflection points enter NONE values of inflection points G List the horizontal asymptotes of f If there are no horizontal asymptotes enter NONE Calculus
Application of derivatives
Consider the function f x 6x 6 List the values of the inflection points of f If there are no inflection points enter NOM Calculus
Limits & Continuity
Consider the function f x x 4x 6 on the interval 0 4 Verify that this function satisfies the three hypotheses of Rolle s Theorem on the inverval f x is on 0 4 f x is on 0 4 and f 0 f 4 Then by Rolle s theorem there exists at least one value e such that f c 0 Find all such values c and enter them as a comma separated list Values of c Calculus
Application of derivatives
Use the graph of the function to answer parts a through f P x x 5 1 a Give the coordinates of the vertex The coordinates of the vertex are 5 1 Type an ordered pair b Give the domain and range What is the domain of P x Type your answer in interval notation 10 8 8 6 4 2 2 Ay Calculus
Application of derivatives
Biologists have observed that the chirping rate of crickets of a certain species is related to temperature and the relationship appears to be very nearly linear A cricket produces 120 chirps per minute at 70 F an 168 chirps per minute at 80 F a Find the linear equation that relates the temperature t and the number of chirps per minute n b If the crickets are chirping at 153 chirps per minute estimate the temperature in F Round your answer to the nearest degree X F Calculus
Indefinite Integration
A spherical weather balloon is being inflated The radius of the balloon is increasing at the rate of 2 cm s Express the surface area of the balloon as a function of time t in seconds Let S 0 0 S t cm Calculus
Limits & Continuity
Express the function G in the form f g There is more than one correct answer The function is of the form y f g x Use non identity functions for f x and g x G x f x g x 1 x 1 Calculus
Limits & Continuity
Find f g h 0 G f x x 2 g x x h x x 2 Calculus
Application of derivatives
Express the function F in the form f g Enter your answers as a comma separated list Use non identity functions for f x and g x F x x 5 8 f x g x Calculus
Vector Calculus
Consider the following functions f x 3x 5 g x 2x 1 Find f g x Find the domain of f g x Enter your answer using interval notation Find g f x Find the domain of g f x Enter your answer using interval notation Find f f x Find the domain of f f x Enter your answer using interval notation Find g g x Find the domain of g g x Enter your answer using interval notation Calculus
Limits & Continuity
Use f x 3x 5 and g x 2x to evaluate the expressio a f f x b g g x Calculus
Vector Calculus
Use the given graphs of f and g to evaluate the expression Assume that each point lies on the gridlines f f 5 y 2 9 0 2 If Calculus
Vector Calculus
Find f g f g fg and f g and their domains f x x x g x x Find f g x Find the domain of f g x Enter your answer using interval notation Find f g x Find the domain of f g x Enter your answer using interval notation Find fg x Find the domain of fg x Enter your answer using interval notation Find 1 x Find the domain of x Enter your answer using interval notation Calculus
Differential equations
Use f x 2x 3 and g x 5x to evaluate the expression a fog 2 b g f 2 Calculus
Application of derivatives
Find the domain of the function Enter your answer using interval notation h x x 7 1 4