Application of derivatives Questions and Answers

ind the general solution given that y e satisfies the complementary equation Use c and c fo he two constants xy 4x 1 2x 1 y 3x e

Find the angle a between the vectors u 3 4 W 5 12 a Round your answer to the nearest tenth Enter

Find the exact value of each trig function below 5 14 sin x y if sin x 54 14 9 cos x sin y 14 4 15 cos x y if sin x cos x 5 54 16 55 2 3 sin y 5 35 tan x y if tan x tan y 4 5 7 10 and cos y 9 and cos y 10 7 11

Write the following equation in logarithmic terms Do not simplify your answer Answer 2 7 19

What is the radius of convergence 9 Find the parametric equation for the cyloid given by a wheel radius 10 meters if i is moving foward at 5 meters per second 10 T 11

Evaluate the following logarithmic expression Round off your answer to two decimal places logis 478

10 Find the area inside r 1 sin 0

Evaluate the following logarithmic expression without the use of a calculator Write your answer as a fraction reduced to lowest terms log 1 1

Solve the following logarithmic equation Express your answer as either an exact expression or a decimal approximation rounded to four decimal places If there is now solution indicate No Solution 0 log x 2 log x 2 1 X Answer How to enter your answer opens in new window If you wish to enter log or In you must use the keypad If there is more than one solution separate your answers with a comma Selecting a radio button will replace the entered answer value s with the radio button value If the radio button is not selected the entered answer is used Keyp Keyboard Short No Solution 8

Write the equations needed to solve each problem Then solve How many steps Answer do 1 Anna plants peas in of her garden and herbs in of it She divides the rest of the garden into 6 sections What fraction of the original garden is each section Equations need to solve you each problem

A certain species of deer is to be introduced into a forest and wildlife experts estimate the population will grow to P 1 630 2 where r represents the number of years from the time of introduction Step 1 of 2 What is the doubling time for this population of deer Answer How to enter your answer opens in new window Keypan Keyboard Shortc

The half life of nitrogen 16 is approximately 7 13 seconds Step 1 of 3 Determine a so that A 1 Aga describes the amount of nitrogen 16 left after 1 seconds where Ao is the amount at time 0 Round to six decimal places Answer How to enter your answer opens in new window Keypac Keyboard Shortcu

1 Find three other pairs of polar coordinates for 4 5 plot the point

Calculate the divergence of the field 12x 7y 8z Calculate the curl of the field 22 32 4 3yz Show all steps

4 Sketch the curve and find a r 3 Cartesian equation a b 0 1

a Cartesion equation for r 6c050 Graph it

3 write this Cartesision equation in standard form Graph it Find a polar equation for it x y 4y 5 0

Tessa invests 5500 in a new savings account which earns 4 2 annual interest compounded continuously What will be the value of her investment after 7 years Round to the nearest cent Interest formulas

5 points he acceleration of an object moving in 3 dimensions is given by a t 0 b where b 0 If the initial velocity is and the initial position is 70 find 0 rrections for the velocity and position in vector notation Show all steps

Find the center vertices foci and the equations of the asymptotes of the hyperbola If an answer does not exist enter DNE x y 1 x y center vertices foci asymptotes x y x y x y x y 4 2 smaller x value y larger x value smaller x value larger x value Sketch the hyperbola using the asymptotes as an aid y 4 2 negative slope positive slope 2 4 X erararas 4 2 y 2 2 2 2 4 X X

Find the maximum and minimum values of the function f x y x 2 4xy 4y 2 2x 4y 3 on the region D defined by x 2 y 2 4

Chester hopes to earn 1200 in interest in 2 8 years time from 24 000 that he has available to invest To decide if it s feasible to do this by investing in an account that compounds semi annually he needs to determine the annual interest rate such an account would have to offer for him to meet his goal What would the annual rate of Interest have to be Round to two decimal places

Let f x be a continuous function on the closed interval a b and differentiable on the open interval a b Prove that if f a f b and f x 0 for all x in a b then there exists a point c in a b such that f c f x for all x in a b x c

The Fashion Store has 8000 available each month for advertising Newspaper ads cost 400 apiece and no more than 30 can be run per month Radio ads cost 200 each and no more than 40 can run per month TV ads cost 1200 a piece with a maximum of 6 availab month Approximately 2000 women will see each newspaper ad 1200 will hear each radio ad and 15 000 will see each TV ad How much of each type of advertising should be used if the store wants to maximize exposure How many newspaper ads should be placed How many radio ads should be used How many TV ads should be run What is the maximum exposure CI

Billy bought a car for 20 000 Most cars tend to depreciate in value over time After one year Billy s car was valued at 15 000 After two years the value of the car was 11 250 What is the function being used

Is it possible to multiply the following matrices A No Yes 2 3 0 3 4 1 0 5 71 B 2 9 Lo 3 51 1 2 3 3

Consider the equation X x a Solve the equation accurate to 3 decimal places by performing fixed point iteration as given b Find an interval a b such that iteration of xn 1 point for any xe a b 2 n is guaranteed to converge to a unique fixe c Show that the given equation is algebraically equivalent to x teration in this form fails to converge In x In 2 Explain why fixed poi

Find the area of the region that lies inside the cardioid r 2 1 cos 0 and outside the circle r 2 J

Consider the function y x x a Determine the domain of the function b Determine intervals of increase decrease c Determine local max min values e Find points of inflection f Determine intervals of concavity C1

This table 0 4 8 12 9 3 3 3 16 20 24 3 3 9 I f x shows several values of a sinusoidal function f x A formula for f x there may be more than one f x

T b The angle of elevation of the sun is decresing at a rate of 0 25 rad h How fast is the shadow cast by a 400 ft tall building increasing when the angle of elevation of the sun is hint use a trig formula since we are working with an angle 6

a The volume of a cube decreases at a rate of 10 m s Find the rate at which the side of the cube changes when the side of the cube is 2 m

The velocity of a particle moving along the z axis is given by f t 15 5t cm sec Use a graph of f t to find the exact change in position of the particle from time t 0 to t 4 seconds hange in position include units

Find the equation of the tangent to the curve for each function at the given point a y 4 sin x at 1 6 b x 4xy y 13 at 2 1 implicit find d

15 20 Finding the Area Under a Curve Find the area of the region that lies under the graph of f over the given interval 15 f x 3x 0 x 2 MA 23 16 f x x x 17 f x x 2 0 x 1 0 x 5 29

Given the tables for k f below find the following w k w f w 0 3 1 2 3 4 5 67 6 7 69 8 9 036NNS9 4 8 2 7 5 1 0 S6NO69 9 0 2 4 7 1 8 5 Average rate of change of k from 8 to 9 Round answers to 3 decimal places as needed Average rate of change of f from 2 to 7 Round answers to 3 decimal places as needed

b lim ln sin x check what is happening first to sin a when then plug into ln x 4 x 20

1 Find the limits x 9 a lim X2 x 3 x 2x 3

The value of a machine V at the end of t years is given by V C 1 r where C is the original cost and r is the rate of depreciation Find the value of a machine at the end of 3 years if the original cost was 1074 and r 0 1 Round to the nearest cent

Jse calculus to find the volume of a pyramid with height h and rectangular base with dimensions b and 26 Volume

piece of wire 6 m long is cut into two pieces One piece is bent into a square and the other is bent into an equilateral triangl a How much wire should be used for the square in order to maximize the total area m b How much wire should be used for the square in order to minimize the total area

10 If cosa 53 2 5 find 3cos a csca cot a

7 Select the expression below that is identical to 2 sina 56 A co D sin A D 8 Use a sum or difference identity to select the exact value of sin 75 55 6 2 B cos 2a 3 2 E cosa na csc a cos a esca B 2 E 6 2 4 C sin 2a C 6 2 4

Use double angle identities to find the exact value of each trig function below 3 5 5 sin 20 if sina cosa 56 8 6 56 s100 5 cos 20 if cos 3 8

ithout using a calculator find the missing angle below 3 tan cot 54 for 0 0 90 52 4 52 sin a cos17 20 for 0 s as 90

Find the area inside the cartiod r 2 2cosx outside r 2

Find the radius of convergence R of the series R 8 2 1 nx n 1 Find the interval I of convergence of the series Enter your answer using interval notation I

7 Which equation matches this description Vertical asymptotes x 2 and y 1 x 2 x 5 intercept x 1 y intercept x 5

Evaluate the given limit and justify the steps that you took to find the limit lim tan 1 x 0 2x sin x X Note The goal of this problem is not just to find the correct answer The goal of this problem and justify all the steps and procedures that are needed to solve this problem For the toolbar press ALT F10 POT

Use the upper and lower sums to approximate the area of the region using the given number of subintervals of equal width Round your answers to three decimal places upper sum lower sum y 1 x 1 1