Differentiation Questions and Answers
Calculus
DifferentiationFind the following for the function f x 4x 2x 4 a f 0 b f 5 c f 5 e f x f f x 1 g f 4x a f 0 4 Simplify your answer b f 5 106 Simplify your answer c f 5 86 Simplify your answer d f x Simplify your answer d f x h f x h
Calculus
DifferentiationFind the following for the function f x 2 1 a f 0 e f x b f 6 1 f x 5 a f 0 c f 6 g f 3x on integer or a simplified fraction d f x h f x h
Calculus
DifferentiationWrite the Mayan numeral as a Hindu Arabic numeral H 11 N 2 3 13 14 5 15 16 The equivalent Hindu Arabic numeral is 7 17 8 www 18 9 19 TE
Calculus
Differentiation1 point The expressions A B C D E are left hand sides of identities The expressions 1 2 3 4 5 are right hand side of identities Match each of the left hand sides below with the appropriate right hand side Enter the appropriate letter A B C D or E in each blank A tan x B cos x C sec x csc x 1 cos x D cos x E 2 sec x 1 sin x cos x 1 cos x 1 sin x 2 tan x cot x 3 sec x sec x sin x 4 sin x tan x 5 sin x sec x
Calculus
Differentiationhon 3 4 2 5 An 3 4 80 E 1 x r1a2 5 4 b lim lim K 8 2 560 4 5 15 pts Algebraically determine the indicated limits Indicate or o for those limits that do not exist x249 3 c lim 1 h 1 a lim h 0 3x 4 2x 5 2
Calculus
DifferentiationUse a graphing utility to approximate the real solutions if any of the given equation rounded to two decimal places All solutions lie between 10 and 10 2x 9 3x 2 Which graph can be used to approximate the real solutions of 2x4 9 3x 2 Use the viewing window Xmin 5 Xmax 5 Xscl 1 Ymin 10 Ymax 10 Yscl 1 A D Q Q Q O What are the approximate real solutions Select the correct choice below and fill in any answer boxes within your choice OA The solution set is Round to two decimal places as needed Use a comma to separate answers as needed DE
Calculus
DifferentiationAn estate valued at 216 485 is to be divided between two sons so that the older son receives four times as much as the younger son Find each son s share of the estate The share of the younger son The share of the elder son ww
Calculus
DifferentiationA computer is on sale for 944 If the original price was reduced by 20 what was the original price of the computer The original price of the computer was 11
Calculus
DifferentiationNow find the value of f x Ax f x Simplify your answer completely f x Ax f x 7x 14x4x 74x 2x 24x 7x 2x 7x 14x4x 7Ax 2x 24x 11 7x 2x
Calculus
DifferentiationProblem 9 1 point Let h x sin x Decompose h x into two functions so that h x f g x f x sin 4 g x Note In order to get credit for this problem all answers must be correct X
Calculus
DifferentiationFind the length of the line segment Then find the midpoint of the line segment Assume that the endpoints of each line segment have integer coordinates The length of the line segment is Xmin 6 Xmax 6 Xscl 1 Ymin 12 Ymax 12 Yscl 2 using radicals as needed
Calculus
DifferentiationFind the distance d P P2 between the given points P and P2 P 2 5 P 3 6 d P1 P2 R
Calculus
Differentiation124 9 8 IN Based on the graph above estimate to one decimal place the average rate of change from x 3
Calculus
DifferentiationListen Determine where f is discontinuous fx 0 and 11 0 only 0 and 11 11 only 11 only x if x 0 11 x if 0 x 11 11 x if x 11
Calculus
Differentiation5 8 3 x2 6 8 3 x 2 11 7 4 2 x 3 8 4 2 x 3 13 4 7 x 3 14 4 7x3 15 10 3 x 2 11 16 10 3 x2 21 6x3 7 22 12 2 4 23 9 7 6 24 9 7 6 Math Help 11
Calculus
DifferentiationLet p x 9 A general quadratic polynomial can be written as q x ax bx c Find the quadratic polynomial q x such that q 0 p 0 q 0 p 0 q 0 p 0 q x Plot the graphs of q and p together near x 0 Describe how the graphs are related
Calculus
DifferentiationFind an equation for the line tangent to the graph of z at 3 86 where z is given by z x 4x 4x 14 y Check your result by plotting the graph of z and the tangent line together
Calculus
DifferentiationQuestion 21 Y of 37 Step 1 of 1 Find the equation in slope intercept form of the line passing through the points with the given coordinates 2 3 3 2 Answer 2 Points
Calculus
Differentiationf x Start by drawing the vertical and horizontal asymptotes Then plot the intercepts if any and plot at least one point on each side of each vertical asymptote Finally click on the graph a function button AND 5r 15 x 2x 15 14 12 10 8 6 195 NA V 4 Lo 2 14 12 10 6 2 2 El 54 6 00 8 10 12 2 4 6 8 10 12 14 X
Calculus
DifferentiationSimplify the exponential expression 16 7a 8a 6 16 7a 8a 6 Simplify your answer Type exponential notation with positive exponents
Calculus
DifferentiationSimplify the exponential expression HI Simplify your answer Type exponential notation with positive exponent
Calculus
DifferentiationMo Simplify the exponential expression 60a b4 12ab 60a4b4 10 10 12ab Simplify your answer Type exponential notation with positive expone
Calculus
DifferentiationX portental expression THEE Type exponential notation with positive exponents
Calculus
DifferentiationVerify the identity 1 cos 6 1 cos CSC 6 Expand the product and then use a Pythagorean Identity 1 cos 3 1 cos 6 1 Use a Reciprocal Identity
Calculus
Differentiationd the proper constant to the binomial so that the resulting trin perfect square Then factor the trinomial 1 30t be the missing term that completes the square 30t amplify your answer Type an integer or a fraction
Calculus
DifferentiationFind the unit vector in the same direction as v v 3i u ai bj ck where a Simplify your answers 1 b and c
Calculus
DifferentiationDivide by first converting each number to scientific notation Write the answer in 0 000035 0 0000002 The answer is Use scientific notation Use the multiplication symbol in the math palette as needed
Calculus
DifferentiationConsider the function w t 10t 20t 30 on 2 t 3 Absolute Maximum value Absolute Minimum value at t If applicable enter coordinates in increasing order of t Enter N in any blank that is not needed at t 3
Calculus
DifferentiationIn the following exercises find each indefinite integra by using appropriate substitutions 328 In x X dx
Calculus
DifferentiationDetermine the domain and range for the relation Answer 2 Points T x y x R and y Z OR Even R Domain OR ON OZ Range ON Even N OZ Even Z
Calculus
DifferentiationAnswer 2 Points X w x X 3 5 Step 1 of 3 Identify the general shape and direction of the graph of this function on the interval o 1 if x 1 if x 1 X X Keyboard S
Calculus
DifferentiationStep 4 of 4 Graph the parabola Answer 2 Points 10 Q x x 4x Points can be moved by dragging or using the arrow keys Points whose positions are related to a moved point will be updated automatically Any or curves will be drawn once all required points are plotted and will update whenever a point is moved Enable Zoom Pan 9 S Key Keyboard Shor 5
Calculus
DifferentiationStep 2 of 2 Determine the domain and range of the graph Answer 2 Points Selecting a button will 10 5 Ay 10 S S 10 Enable Zoom Pan 5 Keyboa
Calculus
DifferentiationConsider the function f x whose second derivative is f x 9x 8 sin x If f 0 3 and f 0 2 what is f x f x
Calculus
DifferentiationConsider the function f x F 2 5 24 8 Let F x be the antiderivative of f x with F 1 0 Compute F 2 26
Calculus
Differentiationstion 2 14 3 points Which is the only function below has a relative minimum O O 5432 1 5 a x 2 3 2 b x 5 4 J 2 1 2 15 7 2 3 4 31 21 1 2 3 5 3 21 6 1 2 3 N 7 1 2 J d x F 4 5
Calculus
DifferentiationQuestion 3 A soccer ball is kicked across a field at an angle of 60 with an initial speed of 69 ft s Determine how far the soccer ball traveled in the air 128ft O212ft 2 pts O 57ft
Calculus
Differentiation13 Transformations e given point is reflected across the line indicated F R across y 1