Application of derivatives Questions and Answers

Problem 7 Let f x 8 x ln x 7 x 7 a Find 16 b Find 22

The boxplot below displays the Grade Point Averages GPA of a random sample of collegiate athletes Do the male or female athletes have more variability in their GPAS Male Boxplot of GPAS Female H 2 5 Female Male GPA 3 5

Find the 31 th derivative of y cos 32 by finding the first few derivatives and observing the pattern that occurs

A table of values for f g f and g is given below 0 B If H z g f x then H 1 A If h z f g x then h 1 x f x g x x g x 1 3 3 1 1 2 2 2 3 CAD 1 food 2 CAR 1 1 1 1

Suppose that Find an equation for the tangent line to the graph of f at a Tangent line 2 452

Let f x 2x 3 f 3 119

5 2 point In the graph below a The red line represents all points whose position vectors are orthogonal to a i e all x such that a x 0 y a X Sketch this picture on a set of axes and label all points with position x such that a x 2 and then again for a x 4

3 2 points Let a 1 2 and b 3 4 and c 1 7 be position vectors for the vertices of a triangle Find the average of the vertex positions and use the properties of vector addition and scalar multiplication to show this is the intersection of the medians of the triangle A median of a triangle is a line segment from a vertex to the midpoint of the opposite side

2 2 points Given position vectors v and w which linear combinations cv dw corre spond to the shaded parallelograms below Your answer should be a set of conditions on c and d a W y V X b W y X

4 2 points Show that each statement below is always true or find a counterexample A counterexample should be a concrete set of vectors or scalar for which the statement is false a projab b c compa comp b b proja cu dv cproj u dprojav d a proj a is orthogonal to b

ctor the trinomial 4 a b 2 11 a b 3

Problem 5 Solve the following equation for x In 12ln x 7 Enter your answer symbolically

Problem 4 Simplify the following expressions a e 3 ln 5 In 1 b log2 48 log 3

Find an equation of the tangent line to the graph y x 2x 2 3 23 y Need Help Submit Answer Read it 0 11 Points Find an equation of the tangent line to the graph of f at the given point f x x 49 7 DETAILS SCALCET9 2 XP 7 004 MI

In 2015 there were approximately 4 141 000 births in a country Find the birth rate in births per minute Assuming a population of 336 million what was the annual birth rate in units of births F people The birth rate in units of births per minute is approximately births per minute Round to the nearest tenth as needed

Jennifer borrowed 3200 from the bank in order to buy a new dune buggy She will pay it of by equal payments at the end of each week for 4 years The annual interest rate is 6 95 Determine the size of payments and the total interest paid Express your answers rounded to the nearest cent Payments Total interest

X f x x 8 x a lim f x x 0 b lim f x x 0 c lim f x x 1 d lim f x x 2 e lim f x X 2 f lim f x x 2 x 0 0 x 2 x 2

S 0 11 Points DETAILS Which of the following functions f has a removable discontinuity at a If the discontinuity is removable find a function g that agrees with ffor x a and is continuous at a If an answer does not exist enter DNE a f x The discontinuity is removable O The discontinuity is not removable g x a 1 x x 6x X 3 O The discontinuity is removable The discontinuity is not removable b f x g x a 3 c f x sin x a Recall that h x means the largest integer that is less than or equal to h x O The discontinuity is removable O The discontinuity is not removable g x

In the figure below AXYZ AACB Find tan B sin B and cos B Round your answers to the nearest hundredth N 24 tan B sinB 36 5 27 5 Y A X B

DETAILS 8 0 11 Points Explain why the function is discontinuous at the given number a Select all that apply 4X 15 SCALCET9 2 5 022 10 x 4 Om fx does not exist lim f x and lim x are finite but are not equal Sketch the graph of the function 4 is undefined 4 is defined and lim f x is finite but they are not equal none of the above a 4 4 5 5 y 6 4 2 2 6F 5 10 15 5 y 6 4 2 4 6F 5 10 15 X 15 10 5 1 1 1

K Suppose that x and y are related by the equation 4x y Differentiate both sides of the equation with respect to x Choose the correct answer below O A dy 8x 2y dx O C dy Bx 2y dx OE 8x 2y 0 0 4 and use implicit differentiation to determine 1 X dy dx OB This test 20 point s possible This question 1 point s possible dy 8x 2y dx COD dy 4 8x 2y 0 dx O F dy dy dx 8x 2y 0

t 2 t 3 V V Need Help Submit Answer 1 x 103 S Read It ii x 101 m s m s 7 0 11 Points The cost in dollars of producing x units of a certain commodity is C x 7 000 10x 0 05x a Find the average rate of change in per unit of C with respect to x when the production level is changed from x 100 to the given value Round your answers to the nearest c DETAILS Watch It Master it SCALCET9 2 7 049 per unit per unit b Find the instantaneous rate of change in per unit of C with respect to x when x 100 This is called the marginal cost Its significance will be explained in a future chapter per unit

Prove the statement using the definition of a limit lim x 0 x 0 Given 0 we need Select such that if 0 Ix 01 Nood Hola Select then Ix 01 Select We have x x Ixl Choose e Then 0 x 01 8 x 01 Select By the definition of a limit I

For the function A whose graph is shown state the following If the limit is infinite enter oo or co as appropriate If the limit does not otherwise exist enter DNE a lim A x b lim A x X 27 lim A X X 2 d lim w 0 e The equations of the vertical asymptotes Enter your answers X

1 0 1 Points Use a table of values to estimate the value of the limit correct to three decimal places If you have a graphing device use it to confirm your result graphically 1 p lim p 1 1 p Need Help DETAILS SCALCET9 2 2 024 Submit Answer 2 0 1 Points 3 Read It DETAILS Determine the infinite limit Watch It SCALCET9 2 XP 2 015

Find an equation for the line tangent to the graph of at the point 1 f 1 f x 4x 5

Find the limit Let q and r represent arbitrary real numbers If the limit is infinite enter co or co as appropriate If the limit does not otherwise exist enter DNE lim x x qx

Find the derivative of f x cos I f x

erentiate F f x tan z 3 sin x 3 cos x

Find the limit If the limit is infinite enter co or co as appropriate If the limit does not otherwise exist enter DNE lim x x X110

lim arctan e 818 Need Help Submit Answer Read It 8 0 13 Points Find the limit If the limit is infinite enter co or co as appropriate If the limit does not otherwise exist enter DNE DETAILS SCALCET9 2 6 037 5 ex lim X 5 6e

6 0 167 3 0 333 A 2 0 2 2 1 4 1 Identify the parent function of the graph depicted in the image L 1 6 powered by desmos

Using Riemann sums with four subdivisions in each direction find upper and lower bounds for the volume under the graph of f x y 1 2zy above the rectangle R with 0 z 1 0 y 3 upper bound lower bound

Values of f x y are shown in the table below x 3x 3 3r 3 6 13 16 y 4 8 10 y 4 5 10 12 y 5 12 14 7 Let R be the rectangle 3 3 6 4 y 5 Find the values of Riemann sums which are reasonable over and under estimates for f f x y dA with Ar 0 3 and Ay 0 over estimate 1 under estimate

Suppose f z y zy and R is the rectangle with vertices 0 0 6 0 6 4 0 4 In each part estimate effs f x y dA using Riemann sums For underestimates or overestimates consistently use either the lower left hand corner or the upper right hand corner of each rectangle in a subdivision as appropriate a Without subdividing R Underestimate Overestimate 1 A b By partitioning R into four equal sized rectangles Underestimate Overestimate

1 point Find the average value of f x y x y over the rectangle R with vertices 3 0 3 7 2 7 2 0 Answer

Values of f x y are given in the table below Let R be the rectangle 1551 6 25ys 3 2 Find a Riemann sum which is a reasonable estimate for ff z y da with Az 0 2 and Ay 0 4 Note that the values given in the table correspond to midpoints yz 1 1 1 3 1 5 2 2 3 0 5 26 7 5 3 0 7 5 1 4

roblem 2 Find all solutions to the equation cos x 3 in the interval 2 5T 4 and A and B only C and 5 D and 7 E only F only G only H I ST

Evaluate the iterated integral f f 4x y dady 2048

e sin 5x dx lick on Part 1 to open the section Enter your answers for the steps in Part 1 then click on Sul answers Once your answers are correct you will be able to open Part 2 Once your answers a or Part 2 you wil be able to open Part 3 Step 1 The first integration by parts In this particular example one can let u be either e or sin 5x We will choose e Fill in t of the table below with the appropriate terms for setting up the integration by parts u e4 du V dx dv 4 sin 5r dr dx Now substitute all of this into the Integration by Parts formula giving

Evaluate the integral using an appropriate substitution 9e9e T dx c C

Evaluate the integral using an appropriate substitution x 1 x 2x dx C

Evaluate the indefinite integral Inx dx 7 c x S

Find the area of the figure A V 4 m 15 m 13 m 6 m

7 Let M t represent the rate at which people enter Macy s department store in people per hour t hours into their Black Friday sale Interpret the statement M 3 5 432 in the context of this problem

3 Let L t represent the number of likes on a social media post t hours after it is posted Interpret the statement L 4 2L 3

6 The graph of y g a is shown Order the following from least to greatest g 1 g 2 g 0 5 g 2 5 5 4 0 1 2

3 A table of selected values is given for a function f f x 11 8 3 4 2 X 5 2 120 7 a Find f 2 h What is the value of when f x

5 The graph of y g a is shown For which value s of is 9 0 0 4

4 The graph of y 9 a is shown Find g 1 76 yol 5