Calculus Questions

Find the values of a and b that make the function f x continuous everywhere 2x a x 3 f x ax 2b b 5x 3 x 3 x 3

Proceeds from Notes Payable On January 26 Bella Co borrowed cash from Conrad Bank by issuing a 120 day note with a face amount of 72 000 Assume a 360 day year a Determine the proceeds of the note assuming the note carries an interest rate of 8 b Determine the proceeds of the note assuming the note is discounted at 8 A

2010 bunt banway SUDIONS upium sit still wolf a ubwop Coo cipium 5 1 Sty wolf 36 it D x2 x J 1 XJ

Use the washer method to find the vo Question Find the volume of a solid of revolution formed by rotating the region bounded above by the graph of f x x 4am below by the graph of g over the interval 2 8 about the x axis Enter an exact value in terms of Provide your answer below

Question Consider the region bounded below by f x 0 8e0 9x above by g x 12 on the left by x 5 and on the right by x 9 x 0 If this region is rotated about the x axis what is the volume of the resulting solid Select the correct answer below Oxf 0 8e09 12 O 0 OAL JT 12 x 9 O JT 2 5 0 8e0 x dx 144 0 64e 8x dx X 9 5 0 64e 8x dx 144 dx

SONO YOU ST f hum und

1 Let f x be the mounthly charge in dollars for using x cubic feet of water Explain the meaing of The statement fC1000 55

6 Consider f x x 2 41 a write an decreasins C of X b find all of the mtercepts of f Curite answers as orderd pairs con cave down on which fis where d write two Statements to describe The long ron end behavior of f

XI is moys Su 4 Z 2 2 6 M 223 1 75 a 24 CDS C Z 2 S E 2 get puls of 26 C x 5 5 x UNO NG S

3 If fcx 3x x and g x 3x 2 find and simplify each of time fonowing a g x 5 b fC3D S c gcf 2 D e

What radical function is represented in the graph f x Simplify your answer 9 3 0 4 4 1 5 X

Question Consider the region bounded by the graphs of f x 0 7e0 7x g x x 6 and x 10 If this region is rotated about the x axis what is the volume of the resulting solid Select the correct answer below 10 2 7 8 0 760 7x d dx 10 2 O Orf 10 6 0 700 7x 9 81 O 0 49e 4x dx X 8 Ox 0 49e 4x 1 dx dx 81

Find g x for g x x 5 4

the washer method to find the volume of a solid of revolution around the y axis Question Let R represent the region bounded on the right by the graph of f y y 2 on the left by the graph of g y and on above and below by y 8 and y 2 What is the volume of the solid of revolution obtained by rotating R about the y axis Enter an exact value in terms of

Find y if y 3 X

Find y if y 2x6 9x5 3 3

2 f x tan 3x for 0 x 2

6 Given the graph of f x find f x dx 7

Find the value s of k such that f x is continuous everywhere x 7 4x3 3kx 2 O f x x 2 x 2

For questions 5 6 use the graph of f x shown below 5 List and explain each type of discontinuity and where it is located 3 5 1 b 8 0 1 2 1 6 Determine whether f x is continuous on the given interval If not explain why a 8 x 4 6 7 C 8 0 8 9

13 Let f be the function defined by f x value of a is f continuous at x 10 x 14x 40 x 10 a x 10 For what x 10

Select True or False for each statement You must get all of the answers correct to receive c 2 2 V V V V In 23 In 25 In 2 In a 5c 5c ln a In x a ln x In 64 In 6 4

Enter a T or an F in each answer space below to indicate whether the corresponding statement is true or false You must get all of the answers correct to receive credit 1 In ab ln a ln b 2 lnx lny 3 ln x y ln x ln y 4 In a b ln a

f x 2 ln sin

The region is formed by the graphs of y 2 x and y 8 x Find the volume of the solid obtained by revolving the region about the x axis 512 The volume of the solid obtained by revolving the region about the x axis is EXIB

A hemispherical bowl of radius 7 inches is filled to a depth of h inches where Oshs7 Find the volume of water in the bowl as a function of h Check the special cases h 0 and h 7 The volume of the water in terms of his V 7 686 3 Type an exact answer using as needed 7h in h 3 in Type an exact answer using as needed What is the volume of water when h 0 V 0 0 in Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression What is the volume of water when h 7 C

Let 1 x 15x and let R be the region bounded by the graph off and the x axis on the interval 0 5 a Find the area of the surface generated when the graph off on 0 5 is revolved about the x axis b Find the volume of the solid generated when R is revolved about the x axis a Find the area of the surface 94 2478 square units Type an exact answer using z as needed b Find the volume of the solid 85 87 cubic units Tyne an exact answer using x as needed CIIS

Find y if y 9 4 x

Find y if y 2x5 3x4 9 2

Find the mass of the thin bar with the given density function p x x 10 x for 0 x 3 2 1 The mass of the thin bar is 10 10 5 5 units 3

Let R be the region bounded by the following curves Use the shell method to find the volume of the solid generated when R is revolved about the x axis y 338 2x in the first quadrant Set up the integral that gives the volume of the solid Use increasing limits of integration Select the correct choice below and fill in the answer boxes to complete your choice Type an exact answer O A OB S 338 0 dx 2 338 y 2 dy The volume is 54925m Type an exact answer

Let R be the region bounded by the following curves Let S be the solid generated when R is revolved about the given axis If possible find the volume of S by both the disk washer and shell methods Check that your results agree y 1 x 1 OB OA JO X 18 y 1 revolved about the x axis Set up the integral s that gives the volume of the solid as a single integral if possible using the disk washer method Use increasing limits of integration Select the correct choice below and fill in any answer boxes within your choice S dx dx Type exact answers I dx Type exact answers

A hemispherical bowl of radius 7 inches is filled to a depth of h inches where 0 sh 7 Find the volume of water in the bowl as a function of h Check the special cases h 0 and h 7 The volume of the water in terms of his in Type an exact answer using as needed What is the volume of water when h 0 V 0 in 3 Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression What is the volume of water when h 7 V 7 in Type an exact answer using as needed

Starting at the same point on a straight road Anna and Benny begin biking with velocities in mi hr given by vA t 2t 1 and vg t 7 t respectively Complete parts a through c below a Graph the velocity functions for 0 t 7 O A Av 1 16 12 8 44 04 0 1 2 3 4 5 6 7 G OB Av t 16 12 8 mile s and Anna rides mile s and Anna rides mile s 4 0 0 1 2 3 4 5 6 7 O C mile s Anna rides farther mile s Benny rides farther Av t 16 124 8 4 V 0 0 1 2 3 4 5 6 7 OD Av 1 16 12 8 4 0 F 0123456 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 OA Since Benny rides OB Since Benny rides OC Anna and Benny both ride Q

Due Wednesday by 11 59pm Submitting an external tool Points 100 CURRENT OBJECTIVE Use the washer method to find the volume of a shifted solid of revolution Question Define R as the region bounded above by the graph of f x 3x 1 below by the x axis on the left by x 1 and on the right by x 4 What is the volum the coli

Use the washer method to find the volume of a shifted solid of revolution Question Define R as the region bounded above by the graph of f x 3x 1 below by the x axis on the left by x 1 and on the right by x 4 What is the volume of the solid obtained by rotating R about the line y 4 Enter an exact value in terms of

imply the integral that gives the arc length of the following curve on the given interval b If necessary use technology to evaluate or approximate the integral y cos 3x for 0 x OA 1 3 sin 23x dx B T O C 0 T 0 1 9 sin 3x dx R S 0 3 cos 3x dx OD 1 9 cos 3x dx a j 0 b The arc length of the curve is approximately 1 e 3x 9 c

a Write and simplify the integral that gives the arc length of the following curve on the give b If necessary use technology to evaluate or approximate the integral y cos 3x for 0 SXS a Which of the following is a simplified form of the integral OA 1 3 sin 3x dx OB 1 9 sin 3x dx S 1 3c0 OD 1 9 cos 3x dx O C 3 cos 3x dx b The arc length of the curve is approximately Bound to three decimal

Use the washer method to find the volume of a shifted solu Question Define R as the region bounded above by the graph of f x 3x 1 below by the x axis on the left by x 1 and on t right by x 4 What is the volume of the solid obtained by rotating R about the line y 42 Enter an exact value in term of it Provide your answer below

Sketch the lines through the point with the indicated slopes on the same set of coordinate axes Point 3 5 S No Solution a 5 10 9 8 7 6 b 3 fa Slopes c d Undefined 10 2 2 3 4 5 6 7 00 40 W 5 89 10 Graph Layers Line 1 Point 1

The tangent line to a smooth curve r t f t i g t j h t k at t to is the line that passes through the point f to g to h to parallel to v to the curve s velocity vector at to User to and r to to find parametric equations for the line that is tangent to the given curve at the given parameter value t to r t in 7 7 tim 7 x In i What is the standard parametrization for the tangent line X y to 7 Z Type expressions using t as the variable

Evaluate lim 2x sin OTH 5x

Suppose f x has the following values X 5 9 f x 5 5 1 2 6 5 f x lim 100 81 000 3 810 Undefined 1 lim z 6 5 f x 1 3 8 0 8 1 lim z 6 5 f x appears to be Undefined 1 3 5 99 5 05 appears to be 5 999 5 005 appears to be 6 8 6 001 4 999 6 01 4 99 6 1 4 9

Evaluate the limit 5x 10x 7x lim 818 4 3x 6x Use oo if the limit is oo and oo if the limit is o

A Ferris wheel is 40 meters in diameter and boarded from a platform that is 2 meters above the ground The six o clock position on the Ferris wheel is level with the loading platform The wheel completes 1 full revolution in 6 minutes How many minutes of the ride are spent higher than 35 meters above the ground

Suppose f x has the following values x f x 912 lim f x appears to be 06 69 8 Undefined 6 4 9 7 7 lim f x appears to be 2 5 8 9 Undefined 06 4 99 7 97 lim f x appears to be 2 5 8 09 Undefined 4 999 7 997 5 6 5 001 5 01 9 03 9 003 5 1 9 3

24 Given lim f x 6 and lim g x 6 evaluate x 1 x 1 lim 6f x 4g x x 1 lim 6 4f x x 1 lim x 1 Ag 2 6f x 4g x 6 4f x lim 6f x 4g x 6 4 x x 1

Evaluate the following limits If needed enter oo for co and oo for oo and DNE if the limit exist 4x lim 2 3 x 3 4x lim 2 3 x 3 4x lim z 3 x 3

Rationalize the denominator 3 10 7 A Written Examp

Factor x 13x 30