# Calculus Questions

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Calculus
Differentiation
dw dt For the given functions a express as a function of t both by using the Chain Rule and by expressing w in terms of t and differentiating directly with respect to t Then b evaluate w 6ye Inz x In 1 y tant z 1 1 dw at the given value of t dt by dw dt
Calculus
Differentiation
40Write a 40 Write your answer as a fraction or a whole or
Calculus
Application of derivatives
A fence must be built to enclose a rectangular area of 5000 ft2 Fencing material costs 1 per foot for the two sides facing north and south and 2 per foot for the other two sides Fin the cost of the least expensive fence The cost of the least expensive fence is
Calculus
Application of derivatives
A fence must be built to enclose a rectangular area of 5000 ft Fencing material costs 3 per foot for the two sides facing north and south and 6 per foot for the other two sides Find the cost of the least expensive fence The cost of the least expensive fence is Simplify your answer
Calculus
Differential equations
A yeast culture is growing at the rate of W t 0 5e0 1t grams per hour If the starting culture weighs 5 grams what I will be the weight of the culture W t after t hours After 3 hours The weight of the culture after t hours will be W t
Calculus
Limits & Continuity
5 Verify that f and g are inverses f x x 7 g x 2x 14
Calculus
Indefinite Integration
Find the slope of the graph of the function at the given point Use the derivative feature of a graphing utility to confirm your results Function Point 0 0 f 0 8 sin 0 0 f 0
Calculus
Vector Calculus
3 85 8 190 9 230
Calculus
Application of derivatives
A baseball diamond has the shape of a square with sides 90 feet long see figure A player running from second base to third base at a speed of 27 feet per second is 24 feet from third base At what rate in ft sec is player s distance from home plate changing Round your answer to two decimal places 3rd ft sec Home
Calculus
Differentiation
y sin In 5x 2x Different
Calculus
Limits & Continuity
uestion z 6 5 4 3 2 1 3 y 4 5 46 3 6 Write an equation for the function graphed above
Calculus
Definite Integrals
Problem 3 Find the arc length of the graph of x e e from y 1 to y 1
Calculus
Definite Integrals
Problem 2 Find the arc length of the graph of y from x 1 to x 3
Calculus
Definite Integrals
Compute the following derivative using the method of your choi cos x5 sin 5x dx cos x5 sin 5x
Calculus
Definite Integrals
Find the arc length of the curve below on the given interval y In x x 1 for 1 x 65 Hint Integrate with respect to y The length of the curve is Simplify your answer
Calculus
Application of derivatives
Use a calculator to make a table to approximate the following limit Confirm your result with l H pital s Rule lim 1 3h h 0 Complete the table below Round to four decimal places as needed h 10 1 10 2 1 h 10 10 4 1 3h h h 10 1 2 10 10 10 4 3 1 1 3h
Calculus
Limits & Continuity
Use a calculator to make a table to approximate the following limit Confirm your result with l H pital s Rule 17 1 X lim X 0 Complete the table below Do not round until the final answer Then round to six decimal places as needed 17 1 17 X 10 1 10 2 10 3 X h 10 1 10 2 10 3 X
Calculus
Definite Integrals
Use the inverse relations between In x and e exp x and the properties of In x to prove the following properties a exp 0 1 b exp x y exp x exp y c exp x exp xy y rational a How can exp 0 be calculated Choose the correct answer below OA Find In exp 0 B Calculate exp 0 as the product of a constant and 0 c Find a value a for which In a 0 and substitute In a for 0 D Calculate the limit of exp x as x approaches 0 X S dt Recall that Inx X dt For what value is Type an exac answer X S dt 0
Calculus
Definite Integrals
Find the volume of the solid generated when R shaded region is revolved about the given line 1 x y 1 x 1 about y 1 The volume of the solid obtained by revolving the region about 1 i 5x
Calculus
Vector Calculus
Determine whether the following statements are true and give an explanation or counterexample Assume x 0 and y 0 a In xy Inx Iny b In 0 1 c In x y Inx Iny d 2 2Inx 1 e The area under the curve y and above the x axis on the interval 1 e is 1 a Choose the correct answer below OA The statement is false because In 35 In 5 In 7 OB The statement is true For x 0 and y 0 In xy Inx In y by the Product Rule of Logarithms OC The statement is false because In 5 In 7 In 5 7 OD The statement is true For x 0 and y 0 In xy Inx In y by the Quotient Rule of Logarithms
Calculus
Differentiation
Compute the following derivative using the method of your choice d cos x4 sin x dx d cos x4 sin x
Calculus
Definite Integrals
Determine the following indefinite integral Check your work by differentiation S5 dr dr
Calculus
Indefinite Integration
Evaluate the following integral Ax dx
Calculus
Application of derivatives
Find the derivative of the function g x 5x 13x 3 et g x 5x 3x
Calculus
Limits & Continuity
Show all necessary work in your solutions Problem 1 Find the arc length of the graph of y x 2 3 2 from x 0 to x
Calculus
Differentiation
Find the derivative of the function g x
Calculus
Definite Integrals
Find the value of T S 2 esin a cos q dq 1 C 2
Calculus
Differential equations
ind a formula for the inverse of the function z f x In 3x
Calculus
Differentiation
ind the derivative of the function x g x 5x 3x
Calculus
Limits & Continuity
Construct a table of values to find the value of the limit from both sides for lim x 2 x 8 2 x
Calculus
Limits & Continuity
Evaluate the following limits a b NOTE If needed enter INF for o and INF for o HINT Look at where the exponential fuction is going in the f 4 lim 200 ex 7 4 lim 2 0 e 7
Calculus
Indefinite Integration
Find the following integral Note that you can check your answer by differentiation S 6e4 3 3 dy
Calculus
Differentiation
Find the following integral Note that you can check your answer by differentiatio S 6e4 y Vy dy
Calculus
Definite Integrals
Find the value of S 2 esin a cos q dq 2
Calculus
Definite Integrals
Find the following integral Note that you can check your answer by differentiation S 7 e2z dx
Calculus
Differentiation
et dy dz 5x y e C
Calculus
Differentiation
Find the derivative of the function f x below f x ln 15 e 9 f x
Calculus
Limits & Continuity
The expression e7 9 6 can be written as ef a where f x is a function of x Find f x f x
Calculus
Application of derivatives
Solve each equation for A Solve In 11x 1 5 for x 0 B Solve e 8 1 3 for x x 3
Calculus
Application of derivatives
The expression e 8 52 can be written as ef 2 where f a is a function of x Find f x f x 0
Calculus
Application of derivatives
Given functions Find 3x g x x 6 h x h x a hog x b State the domain in interval notation x
Calculus
Application of derivatives
5 4 M 2 3 2 3 The minimum degree of the polynomial is 2 The minimum degree of the polynomial is 3 The minimum degree of the polynomial is 4 The minimum degree of the polynomial is 5 The minimum degree of the polynomial is 6 The leading coefficient is positive The leading coefficient is negative Based on the end behavior the polynomial is odd Based on the end behavior the polynomial is even
Calculus
Application of derivatives
Determine the end behavior of f x 5x x 4 x 2 5 x 3 2 Ox y x y E
Calculus
Differentiation
A fireworks mortar is launched straight upward from a pool deck platform 10 m off the ground at an initial velocity of 62 m sec The height of the mortar can be modeled by h t 4 9t 2 62t 10 where h t is the height in meters and t is the time in seconds after launch What is the maximum height Round to the nearest meter do not include units in your answer
Calculus
Definite Integrals
Factor completely using synthetic division 3x 5x 4x 4 given that 2 is a root x intercept value Write the answer in linear factor form You must show work to receive credit
Calculus
Limits & Continuity
A salesperson makes a base salary of 1100 per month Once he reaches 38 000 in total sales he earns an additional 6 commission on the amount of sales over 38 000 Write a piecewise defined function to model the salesperson s total monthly salary in as a function of the amount in sales x
Calculus
Application of derivatives
The monthly profit for a company that makes picture frames depends on the price per frame The company determines that the profit is approximated by P x 50x 80 000x 2500 where x is the price per frame and P x is the monthly profit based on that price Find the price that generates the maximum profit
Calculus
Definite Integrals
Problem 5 Use the method of cylindrical shells to find the volume when the region bounded above by x y and x 2 y and below by the x axis and rotated around the x axis
Calculus
Limits & Continuity
What is the angle measure 52 48 51 equivalent to in decimal degrees Enter your answer rounded to the nearest thousandth of a degree in the box