Application of derivatives Questions and Answers

LCULATOR 3 Find the value of 1 i 6 giving your answer in the form a bi

Find the period y 5 cot x 2 Graph the function H 30 4 5m 4 5m 4 5 A 4 4 30 3 4 5 30 44 442 3

The trigonometric function y tan x has period 2nx n is an integer 2 x nx n is an integer Ox nx n is an integer 2 x 2nx n is an integer 3x 2 2nx n is an integer Sketch a graph of this function on the interval 2 2 10 and the following asymptotes 10

Calculate GDP for an economy with exports of 5 trillion investment of 1 5 trillion consumption spending of 11 trillion imports of 6 trillion and government purchases of 3 trillion

The graph of f x is shown below Estimate and list the value of x where f x has a horizontal tangent 3 X 2 10 9 8 7 6 5 4 3 2 1 3 4 160 2 3 4 5 6 7 8 9 10 q

ermine which of the following is equivalent to the given expression swer Cos 74 COS

Use a calculator to approximate the value of the expression if possible Round your result to two decimal places Enter your answer in radians If not possible enter IMPOSSIBLE arccos 0 35

Find the exact value of the expression if possible If not possible enter IMPOSSIBLE an 3 arctanl

find 6 S s 0 I f x dx 50 0 1 6x dx

2 3 Let n be a positive integer Prove that there is a one to one correspondence preserving multiplicities between the irreducible factors of n as an integer and the composition factors of Z nZ as a group In fact the Jordan H lder theorem may be used to prove that Z is a UFD

Exam x y Y a Find the domain of g x y for g b Sketch the level curves g x y c c 1 0 2 Note Some authors prefer the term contour or contour plot instead of leve curve

Find the area of the parallelogram that has two adjacent sides u 3i j 2k and v 2i 2j k Find uxv uxv 5 i 1 j 8 k Simplify your answer The area of the parallelogram is Simplify your answer Type an exact answer using radicals as needed

The region R in the xy plane is bounded by the graphs of y 2x and y x 6 The centroid of R is located at x y

nd the interest on the following loan 5386 at 2 loan made on August 20 and due December 14 ne simple interest for this loan is Round to the nearest cent as needed

The centroid of the triangle with vertices at 0 0 4 0 and 0 7 is 7

Find the cross product u xv in the figure uxv j k u 3 0 0 X ZA v 0

x Compute uxv if u 4 and v 6 and the angle between u and vis uxv Simplify your answer Type an exact answer using radicals as needed Use integers or fractions for any numb the expression

4 3 2 4 Three roots of a quartic equation x ax bx cx d 0 are x 2 x 3 x i 1 Given that a b c d are real numbers find the values of a b c d

g and Proof K In the figure below the of each variable

A stone is thrown with an initial velocity of 31 ft s from the edge of a bridge that is 44 ft above the ground The height of this stone above the ground t seconds after it is thrown is f t 1612 31t 44 If a second stone is thrown from the ground then its height above the ground after t seconds is given by g t 16t vot where vo is the initial velocity of the second stone Determine the value of v such that the two stones reach the same high point When an object that is thrown upwards reaches its highest point just before it starts to fall back to the ground its bridge use the equation The initial velocity of the second stone would need to be vo Do not round until the final answer Then round to one decimal place will be zero Therefore to find the maximum height of the object thrown from the

An object moves s t 2t 3 3t 2 8 meters where t is in seconds What is the average velocity between t 1 and t 3

Find and simplify the derivative of the following function 8ex 5ex 7 f x Which of the following shows how to find the derivative of f x A F x 5e 7 8e 8e 5 7 Be d dx Bex 5e 7 5e 7 d dx 5ex 7 OB f x Be 7 6 0 Se 7 5ex 7 OD x e de be 7 5 7 OC f x The derivative of f x 8ex 5ex 7 is

Charlie and Rose share a garden Charlie can weed the garden working alone in 90 minutes Rose can finish the task in 75 minutes If they work together how long will it take them to weed the garden

17 tan 80 tan 55 1 tan 80 tan 55 TT 21 sin COS 3 TT 10 cos TT 5 sin 3 T 10

Consider the differential equation 7 A At the point 1 5 1 the direction field has a slope of B At the point 1 1 the direction field has a slope of C Use your answers above to help choose the correct direction field for the differential equation 1 1 X 1 dr 1 1 xy 1 V 1 1 1 12 1 1 ANN 1ANX N1 XX 1 7 7 lall 1 I V 1 1 A Q

onsider the following function tep 1 of 2 Determine the more basic function that has been shifted reflected stretched or compressed swer r x 6 x fl

y f x1 x2 x1 3x2 x1x2 Maximize this function subject to the constraint that x1 x2 6 Clearly write out the Lagrangian and the first order conditions

D Name the property of equality or congruence tha AB BC 12 AB 12 BC

Fill in each box with the co 5 x 9 5 5 5 x 9 5 5 List the terms in the sam

a Verify that the function y x C 28 is a solution of the differential equation ry 2y 4x x 0 b Find the value of c for which the solution satisfies the initial condition y 3 C

7 a 4 Pts What is the domain of the function z f x y ln x y 4 since its en 2 4 00 X 6 7 b 2 Pts Is f x y continuous at all points in its domain You must explain your response A simple YES or NO answer will receive no credit not because hin Yes it includes all the numbers after the number 4 not included to infinite

Bailey flies a drone in a circular path around an object that is 210 feet east and 190 feet south of her position The drone s path takes it over a point that is 160 feet east and 240 feet north of her Find an equation for the drone s path Assume Bailey is located at the origin with the horizontal axis running east west and the vertical axis running north south The drone s path follows the equation x 190 y 210 139400

question below Find the x intercepts of the graph of the equation x 6x y 7y 16 The x intercepts are 10 0 16 0 X Enter the coordinates of the x intercepts If there is more than one intercept separate the coordinates by commas

question below Write the equation for the circle with center 4 3 and radius 2 The equation of the circle is x 4 y 3 49 x Be sure to X enter the equation of the circle

Ernie Rolph dep interest will he e end of one year

5 0 47 Points DETAILS LAR A point is moving along the graph of th

DETAILS The revenue and cost functions for a particular product are giv R x 0 2x 170x C x 72x 9125

Find an equation of the tangent line to the graph at the given point 3 x2 y2 2 100 x y 4 2 y Lemniscate 4 4 2 2 6 4 1 2 2 4 2 4 6 X

3 14 pts Use the graph of f x below to ans a Determine where f x is increasing Pl b Determine where f x is decreasing P c Determine the interval where f x 0 d Determine the local minimum point s e Determine the local maximum point s f Find the x intercept s of f x Please g Find the y intercept s of f x Please v

Find the functions and their domains Enter the domains in interval notation f x 7x 1 g x x x a fog fog x domain b gof gof x domain c fof fof x domain d gog gog x domain

Consider the following 9x 25y2 225 a Find two explicit functions by solving the equation for y in terms of x positive function Y negative function Y2

a Use a graphing utility to graph f x x 4x 2 on the interval 2 2 and approximate any local maxima and local minima b Determine where f is increasing and where it is decreasing a Using a graphing utility graph the function for 2 x 2 and 4sys 10 Choose the correct graph below OA O B Q The local maximum is y and it occurs at x Round to two decimal places The local minimum is y and it occurs at x Round to two decimal places b Where is the graph of f increasing O 1 15 1 15 O 2 1 15 and 1 15 2 O 2 1 15 and 1 08 5 08 O 1 08 5 08 Choose the answer that most completely answers the question Where is the graph of f decreasing Q G O C

The graph of an equation is given a Find the intercepts b Indicate whether the graph is symmetric with respect to the x axis the y axis or the origin 8 6 4 2 2 EN 2 4 6 co 8 Q CITE a Select the correct choice below and if necessary fill in the answer box to complete your choice OA The intercept s of the graph are Type an ordered pair Use a comma to separate answers as needed B There are no intercepts b Choose the correct answer below Select all that apply A The graph is symmetric with respect to the x axis B The graph is symmetric with respect to the origin C The graph is symmetric with respect to the y axis D The graph is not symmetric

DETAILS ng calculator is recommended he an appropriate viewing rectangle for the function and use it to draw the graph x cos x 60 0 1 30

9 1 Points Grades SX Homepage x webassign net web Student Assignment Respor DETAILS Graph the function g x 5 cos x Trigonome y X

Use the formula to deter variable for the values gi Y2 1 determine m X2 X1 X 16 x 2 y 12 a m

Exercise Divide the state into ten subintervals as follows Starting from the top draw horizontal line segments across the width of the state every 1 cm down the state Next measure the widths of each of these line segments in centimeters and label each segment with its width Next use Simpson s Method with n 10 to estimate the total area of the state of Illinois Use the fact that Illinois has a maximum width of 210 miles to determine the scale of the image below

r 2 sin i 2 cos j 3rk 12 136 The position of a particle is defined by seconds Determine the magnitudes of the velocity and acceleration at any instant m where t is in

K Write true or false for the A man might be 2 kild Choose the correct answ O False

olve the equation x 3 2 2x 3 6