Calculus Questions

Differentiate the following function V r V r 43 7

Let f x 2x8 525 3x 5x find f x Answer Find f 1

Find the indicated values for the function f x 4x 8 Select the correct choice below and if necessary fill in the answer box to complete your choice A f 2 0 Round to the nearest hundredth as needed OB The function value is not a real number Select the correct choice below and if necessary fill in the answer box to complete your choice O A f 1 B The function value is not a real number Round to the nearest hundredth as needed Select the correct choice below and if necessary fill in the answer box to complete your choice OA f 1 Round to the nearest hundredth as needed B The function value is not a real number

For the given function find f 23 f 60 f 31 and f 129 f x x 4 Find f 23 Select the correct choice below and if necessary fill in the answer box to complete your choice A f 23 3 Simplify your answer OB The root is not a real number Find f 60 Select the correct choice below and if necessary fill in the answer box to complete your choice A f 60 4 Simplify your answer B The root is not a real number Find f 31 Select the correct choice below and if necessary fill in the answer box to complete your choice L OA f 31 Simplify your answer OB The root is not a real number

Find the following Assume x can repre XXX A

Find the following root 5 1 32

Find the following Assume that the letter 5 5 5 5

Find the following Assume that variables can represent any real number a 5 a 5

For the given function find f 23 f 60 f 31 and f 129 3 f x x 4 Find f 23 Select the correct choice below and if necessary fill in the answer box to complete your choice A f 23 3 Simplify your answer OB The root is not a real number Find f 60 Select the correct choice below and if necessary fill in the answer box to complete your choice A f 60 OB The root is not a real number Simplify your answer

Find the indicated values for the function f x 4x 8 FFF Select the correct choice below and if necessary fill in the answer box to complete your choice A f 6 OB The function value is not a real number Round to the nearest hundredth as needed

Evaluate the following limits If needed enter INF for and INF for a b lim I 00 373 37 11x 7 8x 5x3 3x3 3x 11x lim 2 00 7 8x 5x3

Evaluate the following limits If needed enter INF for o and INF for b 10x 6 1lz 200 3 6x 9 11x T 10x 6 1lz JUNE

A function is said to have a vertical asymptote wherever the limit on the left or right or both is either positive or negative infinity For example the function f x 2 11 has a vertical asymptote at 5 213 x 5 For each of the following limits enter either P for positive infinity N for negative infinity or D when the limit simply does not exist x 1 lim 25 2x 3 x 5 1 I5 2x 3 x x 1 lim 25 2x 3 x 5 5

Let f x 7 x 1 x 3 Use interval notation to indicate the largest set where f is continuous Largest set of continuity 1 0 T

Evaluate the following limits If needed enter INF for oo and INF for a b lim I lim 2 4x 8 5 2 4x

K The number of farms in the United States t years after 1925 is f t million where f t is graphed in Figure A and f t and f t are graphed in Figure B Click the icon to view Figure A Click the icon to view Figure B a Approximately how many farms were there in 1975 million farms Type an integer or decimal rounded to the nearest tenth as needed Figure A 6 5 4 3 2 y 1 0 10 20 y f t 30 40 50 60 70 t X Figure B 0 05 1 Y 10 20 30 40 50 y f t y f t Print b Done 60 Clear all 70 t X Check answ

f 5 4 f x 0 for x 5 f 5 0 and f x 0 for x 5 Choose the correct graph below O A 5 4 Al X Q OB 5 4 O C Ay 5 4 4 D 5 4 X

Which of the functions below are decreasing for all x B A Ay X X D X X Q C O Points 0 of 1 Select the correct choice below and if necessary fill in the answer box to complete your choice A Save Type A B C or D Use a comma to separate answers as needed OB None of the functions are decreasing for all x

3 Find the graph of a function that is defined and increasing for all x 20 has an inflection point at x 8 and is asymptotic to the line y x 15 Choose the correct graph O A Ay 15 N X 0 4 8 12 16 O B 15 X 0 4 8 12 16 O C 15 O X 4 8 12 16 D 15 a X 0 4 8 12 16

Draw the graph of the function y f x that satisfies the following properties Both the function and the slope decrease as x increases Select all graphs that satisfy both properties A X G G C B X C C X G D X

Sketch the graph of a function that has the properties described below f 1 3 f 1 0 concave up for all x Choose the correct graph below O A OE 3 1 1 3 X X OB OF 1 3 1 3 X X Q Q Q OU E O C O G 1 0 X 1 0 X Q O D OH Ay 1 3 3 1 X X Q Q

Let f x y be a differentiable function with f x y c a level curve of f Which of the following statements are true Select all that apply Du f zo yo is maximum when u is tangent to the level curve at zo yo Vf zo yo is orthogonal to the level curve at xo 30 Duf xo 30 0 when u is tangent to the level curve at zo yo Vf zo yo is tangent to the level curve at x0 90 f xo 30 c at every point 2o 3o along the level curve

A line is shown on the zy coordinate plane If 14 k is a point on this line find the value of k to a of 25

Luna is saving up for a pair of noise cancelling headphones She has some money saved up from her birthday and is also babysitting to earn more money The table gives data about the hours Luna has baby sat and the total money she has saved Hours of baby sitting Total dollar earnings 2 3 5 6 87 98 25 117 Write an equation that gives the total money she has saved S after baby sitting for h hours

Given a differentiable function f x y which of the following are correct statements about the directional derivative Duf at a point xo yo Select all that apply The direction u rapidly at xo yo u is a unit vector 2006 Vf xo yo is the direction in which f increases most Duf xo yo f xo yo u Du f x0 30 is always a positive number The maximum directional derivative of fat ro 40 is f 2o 30 T 0 ra a

Which of the following is impossible A Two parallel lines with the same intercept B Two perpendicular lines with the same y intercept C Two horizontal lines with the same slope D A horizontal line with no x intercept

Line I passes through 7 15 and a b for some values of a and b a Find values for a and b so that line is vertical b Find values for a and b so that line 1 is horizontall 1 Find values for a and b so that line I is perpendicular to y z 2

Roscoe had 3 large 1 topping pizzas delivered to his house and paid a total of 40 72 Calliope had 2 large 1 topping pizzas delivered to her house from the same pizza chain and paid a total of 28 73 What is the delivery fee Ignore sales tax

Suppose f x y is a differentiable function satisfying f xo yo 10 and fy 2o yo 5 Then the directional derivative of f at xo yo in the direction of the vector v 4 3 is 10 5 55 9

Describe the set of a values shown below using interval and algebraic notation 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8

Let r t x t y t and z f x y f r t Which of the following dz expressions are equal to Vf r t r t D f r Select all that apply dt f x t y t f x t y t of dx of dy x dt dy dt f r t r t r t

Sketch the graph of the following function and use it to answer the following questions 4 x if a 2 Let f x if 2 x 3 if x 3 x 3 Calculate the following limits Enter DNE if the limit does not exists lim f x TORRENT lim f x I 2 lim f x I 2 lim f x lim f x I 3 lim f x I 3

Let f x x 8 Use interval notation to indicate the largest set where f is continuous Largest set of continuity

Let 2 lim f x 3 lim f x I Sketch the graph of this function and find following limits if they exist if not enter DNE 1 lim f x I 19 4 lim f x I 9 5 lim f x I f x 81 C 6 lim f x OF T2 9 if a 9 if 9 x 9 if z 9

118 Evaluate each of the following expressions Note Enter DNE if the limit does not exist or is not defined a lim F x I 1 b lim F x c lim F x I 1 d F 1 e lim F x z 1 f lim F x I 1 g lim F x

eet 2 12 pts Test the following equation for symmetry Show and label each symmetry test Make sure that you state any types of symmetry that the graph of the equation exhibits x 2y 3y4

For what value of the constant c is the function f defined below continuous on if x 0 8 if z 8 00 f x H T C CI 3 PE

Instructions Show your work to receive full credit on each problem you do not need to show every arithmetic step Use algebraic techniques to solve problems unless otherwise instructed Simplify and circle your final answers 1 10 pts Find the intercepts of the equation y Name x 7x 2 x 3

Let f be a continuous function such that f 5 1 and f 5 1 Using the Intermediate Value Theorem classify the following statements as A Always true B Never True or C True in some cases False in others 1 f 0 0 Answer A B or C 2 For some c where 5 c 5 c 0 Answer A B or C

Let f x 7x 5x 3 Use interval notation to indicate the largest set where f is continuous BEEDRAA KEDAEN Largest set of continuity

6 x 5 Find each point of discontinuity of f and for each give the value of the point of discontinuity and evaluate the indicated one sided limits NOTE Use INF for o and INF for If you have more than one point give them in numerical order from smallest to largest If you have extra boxes fill each in with an x Point 1 C lim f x I C lim f x I CI Point 2 C lim f x I C lim f x I C Point 3 C lim f x I C lim f x f x

determine lim f x I 2 What theorem did you use to arrive at your answer 5x 14 f x x x 10

Let lim f x 0 lim h x 2 lim g x 5 I a I a 20 Find following limits if they exist If not enter DNE does not exist as your answer 1 lim f x h x I X 2 lim f x h x I a 3 lim f x g x IX f x Ia h x 4 lim 5 lim I Ta g x g x 6 lim Isa Ta f x 7 lim h x xa 8 lim h x 1 Ta 1 za h r g x I 9 lim

A function f x is said to have a jump discontinuity at x a if 1 lim f x exists I a 2 lim f x exists I a 3 The left and right limits are not equal Let f x Show that f x has a jump discontinuity at x 10 by calculating the limits from the left and right at x 10 lim f x 210 lim f x x 10 H 5x 2 if a 10 4 if a 10 x 5 SARE Now for fun try to graph f x

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

The answer above is NOT correct Find in terms of the constant a lim h 0 4 a h h V 4a

Let 1 25 x 5 Sketch the graph of this function and find the following limits if they exist if not enter DNE 1 lim F x I 5 2 lim F x I5 3 lim F x

find the domain and range of the function 1 f x 3 x A D R 3 00 C D 0 R 0 3 8 2 1 A D 0 R 00 00 C D 0 1 R 0 0 2 g z B D 0 0 R 3 0 D D 0 R 0 B D 1 0 R 00 00 D D 1 0 R 0

Is point B a local maximum local minimum or neither A local minimum B local maximum C neither A B

12 Using the disk method determine the volume of the solid obtained by rotating the region bounded by y x 4x 5 x 1 x 4 and the x axis about the x axis