Differentiation Questions and Answers
Calculus
Differentiationen 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
Calculus
DifferentiationPart 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
Calculus
DifferentiationUse cross multiplication to solve for the unknown in each of the following proportions 33 5 X 11 50
Calculus
Differentiationour 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
Calculus
DifferentiationQuestion 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
Calculus
DifferentiationPoints 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
Calculus
Differentiationf 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
Calculus
DifferentiationCheck 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
Calculus
Differentiationf 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
Calculus
DifferentiationFind 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
Calculus
Differentiation1 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
Calculus
DifferentiationDetermine 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
Calculus
DifferentiationLet 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
Calculus
DifferentiationFind 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
Calculus
DifferentiationFind 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
Calculus
DifferentiationUse 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
Calculus
DifferentiationConsider 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
Calculus
DifferentiationOn 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
Calculus
DifferentiationListen 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
Calculus
DifferentiationFind a linear equation whose graph is the straight line with the given properties through 2 6 and 1 1 y x
Calculus
DifferentiationDecide 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
Calculus
DifferentiationFind 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
Calculus
DifferentiationEvaluate 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
Calculus
DifferentiationSolve 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
Calculus
Differentiationblem 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
Calculus
DifferentiationFind 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
Calculus
DifferentiationCompute 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
Calculus
DifferentiationA 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
Calculus
DifferentiationDecide 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
Calculus
DifferentiationFind 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
Calculus
DifferentiationFind the limit if it exists using the algebraic method lim x 4 4x O 52 O28 18 10x 4
Calculus
DifferentiationDetermine 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
Calculus
Differentiation2 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
Calculus
DifferentiationGiven 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
Calculus
Differentiation3 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
Calculus
Differentiation2 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
Calculus
DifferentiationConsider 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
Calculus
DifferentiationQuestion 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
Calculus
DifferentiationQuestion 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
Calculus
DifferentiationA 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
Calculus
DifferentiationWhich 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