Differentiation Questions and Answers

Convert the numeral to a numeral in base ten 71 3768

Find 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

Find 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

a Find the slope of the line and b interpret the slope 3 2 e

Write 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

1 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

hon 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

Use 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

An 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

A 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

Now 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

Problem 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

Find 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

Find the distance d P P between the points P and P2 P 2 1 P 4 4 d P1 P2

Find the distance d P P2 between the given points P and P2 P 2 5 P 3 6 d P1 P2 R

124 9 8 IN Based on the graph above estimate to one decimal place the average rate of change from x 3

Listen 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

5 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

Let 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

Find 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

places D Question 4 log2 x log x 3 2 X 1 pts

Question 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

f 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

Simplify the exponential expression 16 7a 8a 6 16 7a 8a 6 Simplify your answer Type exponential notation with positive exponents

Simplify the exponential expression HI Simplify your answer Type exponential notation with positive exponent

Mo Simplify the exponential expression 60a b4 12ab 60a4b4 10 10 12ab Simplify your answer Type exponential notation with positive expone

X portental expression THEE Type exponential notation with positive exponents

Verify 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

Verify the identity cot x csc x cos x

d 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

Find the unit vector in the same direction as v v 3i u ai bj ck where a Simplify your answers 1 b and c

Determine what number the difference is congruent to in mod 3 1 3 1 3 mod 3

Express the number in decimal form without exponents 6 2 106

Divide 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

Consider 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

In the following exercises find each indefinite integra by using appropriate substitutions 328 In x X dx

Determine 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

Answer 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

Step 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

Step 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

FIL Fill in the blank with the appropria When a sample is obtained by dr

K Lines and 2 of 1 through parallel lines 12 are

Consider 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

Consider 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

stion 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

Solve the equati 8 4 smaller value larger value

Question 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

13 Transformations e given point is reflected across the line indicated F R across y 1

exact value of the expression sin 4

exact value of the expression sin 7x 4