Calculus Questions

Consider the graph shown Check all that apply f 1 exists lim f x exists x 1 None of the above

The graph below is the function f x 54 3 2 lim x 1 54327 lim x 1 2 he 72 S Find the following If no value exists enter DNE f x f x 12 lim f x x 1

The graph of y f z has the following features e e f 2 1 lim f x 2 2 lim f x 2 2 2 Which of the following might be a graph of y y f x

The region is formed by the graphs of y 3 2x and y 8 x Find the volume of the solid obtained by revolving the region about the x axis ronion about the x axis is CLE

he region is formed by the graphs of y 3 x and y 4 x Find the volume of the solid obtained by revolving the region about the x axis The volume of the solid obtained by revolving the region about the x axis is PREURE

The region is formed by the graphs of y 3 2x and y 8 x Find the volume of the solid obtained by revolving the region about the x axis The volume of the solid obtained by revolving the region about the x axis is E

Find the length of the following curve 2 y In x x 1 for 10 145 The length of the curve is Type an integer or decimal rounded to three decimal places as needed

Find the mass of the thin bar with the given density function p x x 8 x for 0 x 2 The mass of the thin bar is Gyne an exant porwer units

Write and simplify the integral that gives the arc length of the following curve on the given interval Then use technology to approximate the integra x 2 4 on 3 9 The integral that gives the arc length of the curve is L JOdx

etermine the area of the region shown to the right y x 3 y 6 x 3

Determine the area of the given region The region bounded by y sin X 2 and y cos The area of the given region is Type an exact answer using radicalo X 2 on 3t 5t 2 2

Find the area of the shaded region shown in the figure which is not shown to scale

Determine the area of the region shown to the right CIIS CID y x 5

Starting at the same point on a straight road Anna and Benny begin biking with velocities in mi hr given by VA t 2t 2 and Vg t 5 t respectively Complete parts a through c below a Graph the velocity functions for Osts5 OA Av 0 16 12 8 4 04 0 U 2 3 5 B Av t 16 12 8 4 0 mile s and Anna rides VU mile s and Anna rides VA 2 3 4 5 mile s Benny rides farther mile s Anna rides farther C Av t 16 12 8 4 0 0 1 2 3 4 Q OD b If the bikers ride for 1 hour who rides farther Interpret your conclusion geometrically using the graph in part a Select the correct choice and fill in the answer box es to complete your choice Type integers or decimals A Since Benny rides B Anna and Benny both ride 4 mile s OC Since Benny rides Av 1 16 12 8 4 0 3 4 Q Q

Graph the function over a two period interval y 3 cot x Choose the correct graph below O A OB Ay A O 17 O C Ay O D Ay

Answer the questions about the work of a spring a It takes 70 J of work to stretch a spring 0 2 m from its equilibrium position How much work is needed to stretch it an additional 0 4 m b It takes 70 N of force to stretch a spring 0 2 m from its equilibrium position How much work is needed to stretch it an additional 0 4 What is the work done by a variable force F moving an object along a line from x a to x b in the direction of the force b OA W xF x dx SxF x dx a OB W xF x O c W F x D W F x dx F x dx a The work required to stretch the spring an additional 0 4 meter is 560 joules Type an integer or a decimal b The work required to stretch the spring an additional 0 4 meter is 210 joules Tung an integer or a decimal

Question A solid is formed by revolving the region bounded on the left by y 2x on the right by y In x above by y 6 and below by x axis about the y axis Which of the following gives the volume of the solid Select the correct answer below O y 25e4y dy Ox 25e y dy OT 4e10 1 dy 4e10y dy 1 2

Graph the function over a one period interval y cot 2x Which graph below shows one period of the function O A 6 GF G B O C A O D Ay 6 1 1131

Question Consider the region bounded by the graphs of y 7x y ln x y 6 and the x axis If this region is rotated about the y axis what is the volume of the resulting solid Select the correct answer below 6 Of y e dy Oxf 4 46 dy Oxf et y dy J

Give a formula for a function f that satisfies lim f x o and lim f x 0 x 10 x 10 Choose the correct answer below X 1 X 10 OA f x OB f x x 10 x 11 OD f x x 10 x 1 OC f x 2 x 11 X 10

Choose the appropriate description of the following function y 4sin 6x 7 Which of the following is the appropriate description of y 4sin 6x 7 1 OA amplitude 4 period phase shift 7 OB amplitude 7 period 3x phase shift 4 7 OC amplitude 4 period 3x phase shift 6 O D amplitude 4 period 3 phase shift 6

Find the a period b phase shift if any and c range of the following function y 3 sec X R 2 T a The period is Type an exact answer in terms of b Select the correct choice below and fill in the answer box within your choice OA 3 3 OC 0 00 OA The phase shift is OB The given function has no phase shift c Find the range of the function Choose the correct answer below units Type an exact answer in terms of t OB 3 U 3 OD 3 U 3

PROBLEM 6 For a function f R R f x xe 5x 3p find the right sided slant asymptote 5p examine the monotonicity and find local extreme values 2p verify if it is injective

y square root of 4 x 2 y 0

Determine the point on the graph of the unit circle that corresponds to T findcos 2 andsin COS T and state which functions are undefined for The point on the unit circle is Type an ordered pair Type an integer or a simplified fraction The functions that are undefined for 2 2 are RIN and 2 T T 2 0 Simplify your answer sin Simplify your answer RIN 2 Then 1 0 2 Ay 2 0 1 10 1 0 1

Question Consider the curve f y y Jour for 1 y 2 Find the arc length of the curve 4y

K Find the circular function values for the given number s State which functions are undefined for s Do not use calculator 3x 2 S A sin 3x 2 A cos OB The function is undefined Select the correct choice below and if necessary fill in the answer box to complete your choice Type an integer or a fraction 3r 2 Type an integer or a fraction 1 0 2

Choose the correct graph of the function y 2cos x Choose the correct graph below O A N Ay 10 G OB 10 Q O C Ay 10 Q OD 10 10

Use transformations to graph the following function y 4 sinx Select the graph that represents the given function O A Ay K 2x G OB K 2x G O C Ay 10 21 G O

t the following radian measure to degree measure

Question Consider the curve f y 6y 1 over the interval 2 y 6 Which of the following integrals represents the arc length of the graph of f y Select the correct answer below O 6 24y 1 dy 6 6y 1 dy 576y 1 dy 6y 2 dy 6y 1 1 dy

Calculate the amount of work done to lift an object and cable Question How much work in foot pounds is done when a 45 foot long cable with a weight density of 7 pounds per foot is wound up 34 feet Do not include any units in your answer

The formula 0 can be rewritten as 0 wt Using wt for 0 changes s r0 to s rot Use the formula s rot to find the value of the missing variable t T s 5 cm r 4 cm w radian per sec 8 t sec Type an integer or a fraction

Let x y be any two vectors in space Which of the following are properties of the cross product x x y Select all that apply x x y is orthogonal to the plane determined by x and y xxy y xx x xx y 0 and y x x y 0 Oxxy y x x x x y is the area of the paralellogram determined by x and y Oxxx yx y 0

Convert the following degree measure to radians 90 90 radians Simplify your answer Type an exact answer u

The concentration of a solution is defined as the amount of a substance divided by the volume of the solution Suppose a vat contains 18 kg of salt and 50 liters of water At t 0 water is added at a rate of 25 liters minute while salt is added at a rate of 9 kg minute A function giving the concentration after t minutes will be C t kg liter express as a function of t As time passes the concentration will Decrease Increase

The graph below is the function f x 5 4 3 2 1 3 2 7 lim H 2 f 2 f x 2 123 4 5 lim f x x 2 lim f x x 2 1 1 Q Find the following If no value exists enter DNE C 2 3 4 5

lim sin x 4 sin 4 0 H 0 sin x 4 sin a cos 4 cos x sin 4 sin r sin 4 cos x cos 4 sin r sin 4 cos z cos 4 sin z cos 4 cos z sin 4 So sin 4 sin 4 So sin x cos 4 sin 4 cos r 1 sin r cos 4 cos x sin x sin x 4 sin 4 H 0 sin z cos 4 sin 4 cos z 1 sin 4 lim 2 0 H sin 4 H sin z 4 H 1 sin 4 H lim 2 0 sin x cos 4 K O lim 2 0 Part 2 of 5 Part 3 of 5 Part 4 of 5 Part 5 of 5 sin 4 cos z 1

lim sin 2 4 sin 4 2 0 sin x 4 sin z cos 4 cos z sin 4 sin z sin 4 cos z cos 4 sin a sin 4 cos z cos 4 sin z cos 4 cos z sin 4 So sin 4 sin 4 sin z cos 4 sin 4 cos z 1 sin z cos 4 cos z sin 2 sin z 4 sin 4 F So 0 sin z cos 4 sin 4 cos z 1 Um z in 4 z z lim sin z cos 4 lim Part 2 of 5 Part 3 of 5 Part 4 of 5 Part 5 of 5 sin 4 cos z 1

Suppose 0 If 2 then lim x 0 lim 0 lim sin u sin u 0 u lim H 0 U sin 2x I sin 2 1 2 2 2 U 2 OF OF X

Question Consider the curve f x x 1 for 1 x 4 Find the arc length of the curve 2x Enter an exact answer Provide your answer below

Which of the following is equal to 2x 3x 2x sin 2x 2x sin 3x 3x sin 2x 3x sin 3x 2 sin x 3 sin x sin 2x 3x sin 2x 2x Which of the two expressions can be multiplied to obtain more expressions 2x sin 3x 3x sin 3x sin 2x lim 2 0 2x sin 2x sin 3x 2z lim 2 0 sin 32 assume x0 Select all that apply Part 1 of 3 2x sin 2x 2x sin 3x Part 2 of 3 Select two or Part 3 of 3

Let f x be the number in thousands of computers sold when the price is x hundred dollars per computer Interpret the statements f 14 80 and f 14 2 Then estimate the number of computers sold if the price is set at 1425 per computer T What does f 14 80 imply O A When the price per computer is 1400 for every 100 price increase the sales increase by 80 000 computers OB 80 000 computers are sold when the price is set at 1400 OC When the price per computer is 8000 for every 100 price increase the sales increase by 14 000 computers OD 80 000 computers are sold when the price is set at 140

Use the washer method to find the volume of a solid of revolution around Question 2 A solid is formed by revolving the region bounded by the graphs of f x 0 3e0 x g x x 2 and x 7 about the x axis Which of the following gives the volume of the solid Select the correct answer below Oxf 0 09e xx dx 0 0 09e 46 dx 2 0 6 0 3e0 dx

Suppose that f 600 6000 and f 600 10 Estimate each of the following a f 601 b f 600 5 c f 599 d f 598 e f 599 75 a f 601 Simplify your answer Type an exact answer

Suppose a student finds the following values of x and f x x If f X 1 9 10 1 99 344 1 999 8197 L these values would make us DOUBT the claim that lim f x x 2

An object moving in a straight line travels s t kilometers in t hours where s t 7t 5t a What is the object s velocity when t 6 b How far has the object traveled in 6 hours c When is the object traveling at a rate of 6 km h a The object s velocity when t 6 is km h

Find the mass of the following thin bar A 5 m bar with a density in g m of p x 250c For a thin bar or wire represented by the interval a sxsb with a density function p with units of mass per length what is the mass of the object d OA m P x dx OB m m b Sp x dx 8 d dx P x OC m for 0 x 5 b OD m xp x d Sxp x dx

Consider the cost function C x 7x2 12x 24 thousand dollars a What is the marginal cost at production level x 5 b Use the marginal cost at x 5 to estimate the cost of producing 5 50 units c Let R x x 41x 36 denote the revenue in thousands of dollars generated from the production of x units What is the break even point Recall that the break even point is when the revenue is equal to the cost d Compute and compare the marginal revenue and marginal cost at the break even point Should the company increase production beyond the break even point a The marginal cost at production level x 5 is C

Ay 01 0 3 0 y f t y f t 10 12 14 16 8 Years after 1980 Q OU Q ndituror in billions of dollars The red Next question National health expend dollars from 1980 to 1994 are given by the function f t in the graph to the left a How much money was being spent at the beginning of 1983 billion