Vector Calculus Questions and Answers

Use a calculator to complete the following table to five decimal places n 10 100 1 000 10 000 100 000 1 000 000 10 000 000 00 1 er 2 59374 e 2 718281828459 CH Complete the following table Round to five decimal places as needed n 10 100 1 000 10 000 100 000 1 000 000 10 000 000 1 in n 2 59374

14 Find the horizontal asymptotes to Hoid 192 LAS A y 2 amwollol B y 1 C y 0 D DNE

1 2 12 14 Final Sum Factor each completely 1 16x 36x 70 A 2 2x 7 4x 5 B 2 2x 7 4x 5 C 4x 7 2x 5 D 2 4x 7 2x 5 Simplify each expression 2 M 3 A 3 2 2m 1 e LLC All rights 3 3 20

5 4 The function f is given by f x x 2x The function g is the result of a transformation of f and is given by g x 2x 4x Which of the following describes the transformation of the graph of f whose image is the graph of g A A vertical dilation by a factor of 2 B A horizontal dilation by a factor of C A vertical dilation by a factor of 2 D A horizontal dilation by a factor of 2 KOBUS The rational function f is given by f x x 3x 1 Which describes the end behavior of f 2x 3 A lim f x and lim f x 8118 x48 o and lim f x X18 B lim f x X118 C lim f x o X118 and lim f x 0 818 IN D lim f x and lim f x 00 8118 X 80

10 275 X

9 455 X

21 sin 150 X

10 275

19 cos 0 1020

os 0 300

17 tan 0 315

1 A conical paper cup 3 inches across the top and 4 inches deep is full of water The cup springs a leak at the bottom and loses water at the rate of 2 cubic inches per minute How fast is the water level dropping at the instant when the water is exactly 3 inches deep Express the answer in inches per minute

5 The length of a solid cylindrical cord of elastic material is 32 inches A circular cross 1 section of the cord has radius inch a What is the volume in cubic inches of the cord

4 Let f x 3x 2 a Determine algebraically whether the function is even odd or neither 31 1 bus S 81 olev giwollel b Find the difference quotient f x h f x wolod bobryong bing ads sall biamo 0

39 40 Find the vectors T N and B at the given point 39 r t 1 1 1 1 3 1

13 16 a Find the unit tangent and unit normal vectors T t and N t b Use Formula 9 to find the curvature 13 r t t 3 cos t 3 sin t

e6x 5x e OA 0 924 OB 0 636 OC 0 778 O D 2 196

sec tan OA 3 OB 2 O C O D 1 5 3 2 2 3 3

K Solve the equation for solutions in the interval 0 2 3 sec2x 9 secx 2 4 A OB O C OD 2n 4x T 3 3 5t 7x IC 6 6 7x 3x 11x 62 6 2x 4x 3x 3 3 2

Choose the equation that matches the rational function graphed 10 8 6 4 6 X 8 10 5 OA OB O C O D f x f x f x f x x x x 6 x x x 6 x x x 6 x x x 6

Solve the equation and express the solution in exact form In ex In e In e9 OA 18 OB 7 O C 11 OD 7

f x OA 2 if x 1 4 xif x 1 5 B OC OD G

3 For the following differential equation 27 y ry x 5 y 0 do the following a Show that r 0 is a regular singular point b Find the indicial equation and the indicial roots of it c Use the Frobenius method to find two series solutions of the equation Show the full explanation for this problem

Compute the surface area of revolution about the x axis over the interval y x ln x 1 e

27 tan 3

Find the x and y coordinates of this function s relative extrema f x 2 X 4 skip Relative Minimum at 2 0 Relative Maximum at 6

D 41 Find m B B 18 ft A 34 11 ft C Syab Xcos DE 42 Find m A A 28 km 34 C B 25 km

1 47 cos COS

46 sin 2

09 10 3 3

y 30 X

5 3 60 X

39 cos 0

30 y 60 10 X

44 tan 0

45 cos 1

39 cos 0

37 cos 2

33 V 45 u 5 2 2

Find the area of the shaded region r 4 3 sin 0 5 y S 5 X

Suppose h is a function such that h 3 3 h 3 3 h 3 4 h 5 7 h 5 6 h 5 12 and his continuous 5 everywhere Evaluate h u du

Write the sum using sigma notation 4 5 6 15 15 k 4

Find the sum 6 k 2 24 1

Divide using long division 3 8m 51m2 27m 56 m 7 OA m 6m 7 2 OB m 5m 8 2 OC 8m 5m 8 OD 8m 5m 8

Write the first five terms of the arithmetic sequence a 12 d 2 OA 12 10 8 6 4 OB 16 13 10 7 4 OC 0 12 10 8 6 D 12 10 8 6 4

Find and simplify the difference quotient f x 6 OA O OB 1 OC 1 OD 6 12 h f x h f x h h 0 for the given function

Find the sum of the infinite geometric series if it exists 8 0 1 1 i 1 OA OB O C OD 80 11 80 9 80 80 9

Find the domain of the rational function f x X 2 x 2 25 OA xx 5 x 5 OB xx0 x 25 OC all real numbers OD xx 5 x 5 x 2

Write the first five terms of the arithmetic sequence O A OB O C O D 5 7 d 5 SIG 5 7 5 7 5 7 7 7 7 2 7 mit 3 1 C 113 10 15 20 7 7 7 7 7 www 7 11 www BE 11 3 7 7 HON 11 7 7 21 22 15 7

Use properties of logarithms to condense the logarithmic expression Write the expression as a single logarithm whose coefficient is 1 Where possible evaluate logarithmic expressions log a9 logar 4 log ap OA log a 4qp r OB loga ap OD log 4 qp OC log an q