Differentiation Questions and Answers

en table indicates the transactions for one teller for one e probability that a customer cashed a check given that stomer made a deposit Type an integer or a simplified fraction Transaction Cash Check Make Deposit 25 No Deposit Total 15 40

Part 1 of 2 08 1 A and B be independent events with P A and P B Find P An B and F O Points 0 of THE

any 2 card hands are possible with a 26 ca mber of hands is

Use cross multiplication to solve for the unknown in each of the following proportions 33 5 X 11 50

a calculator to evaluate 29C plify your answer Type an integer or a fraction

a calculator to find the value below 75P calculator will display the answer

our coins are tossed and the number of heads is recorded Shade the region on the histogram dicated probability x 2 hoose the correct histogram below A 05 038 0 25 0 30 0 25 0 13 0 OB OD 05 036 0 25 0 13 0 34 0 30 0 25 0 13 04

Question 18 8 5 7 O Points cards are drawn without replacement from an ordinary deck Find the pr that the first is not a black card is the conditional probability Type an integer or a simplified fraction

Points 0 of 1 n playing American roulette the croupier attendant spins a marble that lands in one of th able The slots are numbered 1 to 36 with two additional slots labeled 0 and 00 that are p e spin of the roulette wheel is made Find the probability of winning with the given bet xample of a line bet is betting that the marble will land in a slot numbered 6 7 8 9 10 on probability of winning with the given line bet is e an integer or a simplified fraction

0 Simplify the expression 1 point p p q q O 2 30 32 00 1

Multiply 5 Write your answer in simplest form 20

f x and the following A f 3 B g 0 g x x 4 C If f x 28 then x D f g x E f g x F fog x G f g x H What is the domain of f g x

Check out the graph of y f x pictured here Assume that each portion of the graph of f is a straight line as pictured 4 b 2 a State all the values of a for which lim f x does not exist HIG 01 2 3 4 3 30 H 2 36 o 1 2 3 b State all the values of a for which f is not continuous at a 2 c State all the values of a for which f is not differentiable at a 2 Do

sin 80 0 0 sin 90 Evaluate lim

Find the following limit lim x 5 x 3x 11x 5 x 5 x3

f x Calculate the limits of f x as x approaches and co Give exact answers Use symbolic notation and fractions where needed lim X118 3x x lim 818 3x x X 3x x X 11 Find the horizontal asymptote s of f Give your answer as a comma separated list of equations Express numbers in exact form Use symbolic notation and fract where needed horizontal asymptote s Determine the correct statement about the horizontal asymptote s The graph of the function coincides with the horizontal asymptote s The graph of the function crosses its horizontal asymptote s finintely many times The graph of the function never crosses its horizontal asymptote s

Find all values of x where tangent lines to y x4 and y x are parallel Give your answer in the form of a comma separated list Use symbolic notation and fractions where needed

1 Let f x Calculate f x f 5 f 5 h f 5 and x 5 h Express numbers in exact form Use symbolic notation and fractions where needed f x f 5 x 5 f 5 h f 5 h f 5 Take the appropriate limit to find 5 Give an exact answer Use symbolic notation and fractions where needed

Determine f a for a 2 4 7 y 54 4 3 2 1 1 2 3 4 5 6 7 8 9 Give exact answers Use symbolic notation and fractions where needed Enter DNE if the derivative does not exist 2 4 7

Let f x 2x Compute f 3 h Use symbolic notation and fractions where needed f 3 h Compute 3 f 3 Use symbolic notation and fractions where needed f 3 h f 3 Compute f 3 by taking the limit as h 0 Give your answer as a whole or exact number

Find the horizontal asymptotes of f x 3x 4x 4x 2 Use symbolic notation and fractions where needed If there are more than one horizontal asymptote give them as a comma separated list Equation s

Find the Eigen values and Eigen vectors of 3 A 6 2 6 2 7 4 4 3

Find the set of solutions for the linear system 3x1 6x2 x1 x2 x3 3x3 5x2 7x3 Use s1 s2 etc for the free variables if necessary 14 7

Use the graph given above to find the slope and equation for the line Give the slope as an integer or fraction no decima a The slope of the line is m b The equation of the line is y Note You can earn partial credit on this problem

Consider the following function f x x 5 x 5 Find the inverse function f 1 f x State the domain and range of f Enter your answers using interval notation domain range State the domain and range of f 1 Enter your answers using interval notation domain

On a rectangular piece of cardboard with perimeter 11 inches three parallel and equally spaced creases are made See Figure 1 The cardboard is then folded along the creases to make a rectangular box with open ends See Figure 2 Letting represent the distance in inches between the creases use the ALEKS graphing calculator to find the value of x that maximizes the volume enclosed by this box Then give the maximum volume Round your responses to two decimal places Figure 2 Figure 11

If f 0 4 f 0 3 g 0 1 and g 0 6 determine t g U O 11 O 12 O 3 Oo

Listen Differentiate g t t5 cos t Ogi t t4 cos t t5 sin t Ogi t t4 cos t t5 sin t g t 5t cos t t sin t Ogi t 5t4 cos t t5 sin t Ogi t 5t4 cos t 5t4 sin t

Find a linear equation whose graph is the straight line with the given properties through 2 6 and 1 1 y x

Decide which of the two given functions is linear and find its equation X 0 1 Select f x g x 9 10 15 7 2 10 13 3 16 14 4 19 19

Find the point s at which the function f x 6 6x equals its average value on the interval 0 6 The function equals its average value at x Use a comma to separate answers as needed

Evaluate the upper and lower sums for f x 6 x 2 x 2 with n 2 4 and 8 Illustrate with diagrams like Figure 14

Solve the following inequality Graph the solution set 13 2x 7 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution set is Type your answer in interval notation OB There is no real solution

blem 6 S4 f t 4 0 t and assume that when f t is extended to the negative t axis in a periodic manner the resulting function Consider the following differential equation d x 3 4 2 6x f 1 dt2 xp t t 2 Find a particular solution of the above differential equation of the form g t n n 1 An cos t no n 1 and enter the function g t n into the answer box below Enter your answer as a symbolic function of t n as in these

Find the center and radius of the circle x 4 y 4 center x y radius Sketch its graph 6 4 2 2 y 2 X X y 4 X 6 4 2 y 2 y 2

Compute the derivative of the given function and find the slope of the line that is tangent to its graph for the specified value of the independent variable f x x x 16 f x x m f x m 2 1 O f x 2 x m x m f x m 2

A family has three children Let W be the number of boys in the family A box contains three colors of marbleswhite black and yellow Three balls are picked one at a time with replacement Let U be the number of yellow marbles that appear

Decide if the given function is continuous at the specified value of x f x x3 9x x 4 at x 0 lim O No x 0f 0 lim O No x0 f 0 4 lim O Yes x0 f 0 4 lim O Yes x0 f 0

Find O lim 1 00 6 53 f x 3x 8x 5 O lim x too lim x too lim x too f x and lim x too lim 1118 5 lim f x 3x f x 00 f x lim 818 5 lim 3 X40 6 lim f x 3x f x If the limiting value is infinite indicate whether it is or 0 5 f x 3 f x 00 f x 5 3 6 f x 3

Find the limit if it exists using the algebraic method lim x 4 4x O 52 O28 18 10x 4

Determine whether the limit exists If it exists find its value lim x 1 f x 5 4 3 2 1 O 0 3 1 2 515x Ni 3 2 04 1 2 3 Does not exist 4 3 1 2 3 4 15

2 Find the local max min absolute max min if they exist Yes it has a hole Local min s Local max s Absolute min Absolute max 0 f X

Given 1 f5 f x dx 10 and f f x dx 7 1 find 4 f5 f x dx None of the above 07 01 O 3 D

3 Given the points P 1 1 2 Q 3 3 2 and R 2 1 4 find the fourth vertex of the parallelogram with adjacent sides PQ and QR

2 The center of a sphere in 3 space is P 2 6 8 and it is tangent to the yz plane Write its equation in center radius form

Consider the following function 1 x 3 Determine whether f x approaches o or coas x approaches 3 from the left and from the right f x a lim f x X 3 b lim f x X 3

Question 2 4 Listen Ifg x 3 5x use the definition of the derivative to determine g ix g x 3 5x 2 Og x 3 5x 2 g x 3 5x 1 2 g x x 2 None of these

Question 4 0 5 points Listen Use the definition of the derivative to determine f x forf x x 7x x 7x 7 Of x 3x 7 Of x 3x Of x 3x 1 Of x 3x 2

A microbiologist has 6 877 microbes growing in culture when he checks again after fifteen minutes there are 8 224 microbes in the same culture Estimate the difference between the number of microbes at each check by rounding each number to the nearest ten Submit Question

Which of the following are true statements Mark all that are true Olim f x 3 implies that lim f x 3 x a xia Olim f x 3 implies that lim f x 3 x a x a Olim f x 3 implies that lim f x 3 x x a lim f x 3 implies that lim f x 3 x a x lim f x 3 and lim f x 3 implies that lim f x 3 x a x a x a Olim f x 3 implies that lim f x 3 x x a Olim f x 3 and lim f x 3 implies that lim f x 3 x a x lim f x 3 and lim f x 3 implies that lim f x 3 x a x a x a Olim f x 3 implies that lim f x 3 HIP I at