Calculus Questions

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

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

Solve the following logarithmic equation using a calculator if necessary to evaluate the logarithm Write your answer as a fraction or round your answer to two decimal places e 2 7183 In 3x 5 5

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

Use the properties of logarithms to condense the following expression as much as possible writing the answer as a single term with a coefficient of 1 All exponent should be positive 4 In In xy Answer If you wish to enter log or In you must use the keypad K Keyboard S

2 n 1 7 Find the Maclaurin series for cos x x sin x What is the radius of convergence 8 Use Maclaurin series to find

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

8 Use Maclaurin series to find What is the radius of convergence sin x convergence

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

10 Find the area inside r 1 sin 0

2 Find the surface area and volume if y is rotated around the x axis from 1 to 4 3 Find the following integrals a

In an effort to control vegetation overgrowth 74 rabbits are released in an isolated area free of predators After 2 years it is estimated that the rabbit population has increased to 666 Assuming exponential population growth what will the population be after another 6 months Round to the nearest rabbit Answer How to enter your answer opens in new window Keyp Keyboard Short

Find the following integrals a E 2 r sin 4x dr

Eva invests 6700 in a new savings account which earns 5 8 annual interest compounded continuously What will be the value of her investment after 3 years Round to the nearest cent

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

Use the elementary properties of logarithms to solve the following equation Write your answer as a reduced fraction or round your answer to four decimal places if necessary If there is no solution write for your answer Answer log 6x 8 2 Keypad Keyboard Shortcut

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

5 points Find the 4 second partial derivatives of g u v tan u Just state your answers You must use correct notation to receive full credit Fyi that s inverse tangent

Given the function z cos find the domain and the equations for two level curves Show all steps

Compute the directional derivative of the function g x y sin x 3y at the point P 1 3 in the direction of 13 Be sure to use a vector for the direction vector Show all steps

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

Show the following vector field is conservative Then find its potential function F 2e cos y 2e sin y Show all steps

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

7 Sketch the curve on polar graph paper a r 0 b sin 20 c 1 coso d r 1 cos 20

Find the flux of the vector field e 3z xy across the curved sides of the surface S x y z z cos y y 1 0 z 3 Nom vectors point upward

Jose hopes to earn 600 in interest in 2 3 years time from 12 000 that he has available to invest To decide if it s feasible to do this by investing in an account that compounds monthly 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 Interest formulas

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

5 sketch the curve and find a polar equation b y 3 a y x c x y 8

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

Martha invests 7600 in a new savings account which earns 3 8 annual interest compounded monthly What will be the value of her investment after 5 years Round to the nearest cent Interest form

5 points ind the domain of the vector valued function 97 3447 Show all steps Express your answer in interval notation

Find two vectors orthogonal to the plane formed by a 4 5 1 and 2 0 3 Show all steps

Given z V 2x 3y x st y t s find and using the chain rule for 2 independent variables Show all steps

bints ulate the work done pulling a sled 20 m along horizontal ground with a constant force of 10 N at an angle of 55 above the horizontal Show all step

Tessa has recently inherited 9700 which she wants to deposit into an IRA account She has determined that her two best bets are an account that compounds annually at an annual rate of 4 6 Account 1 and an account that compounds semi annually at an annual rate of 2 9 Account 2 Step 1 of 2 Which account would pay Tessa more interest nh

The half life of radium 226 is approximately 1 600 years Step 1 of 3 Determine a so that A t Apa describes the amount of radium 226 left after t years where Ag is the amount at times 0 Round to six decimal places Answer Keys

The function C 1 Co 1 r models the rise in the cost of a product that has a cost of Co today subject to an average yearly inflation rate of r for 1 years If the average annual rate of inflation over the next 14 years is assumed to be 2 5 what will the inflation adjusted cost of a 111 300 boat be in 14 years Round to two decimal places

The function C Cell r models the rise in the cost of a product that has a cost of Co today subject to an average yearly inflation rate of r for years If the average annual rate of inflation over the next 14 years is assumed to be 2 5 what will the inflation adjusted cost of a 111 300 boat be in 14 years Round to two decimal places

id the center vertices and foci of the hyperbola 2 16 223 25 center vertices foci x y x x x y x y x y 10 Find the asymptotes of the hyperbola Enter your answers as a comma separated list of equations 10 Sketch its graph using the asymptotes as an aid Use graphing utility to verify your graph y y 10 10 10 10 10 10 10 y smaller x value 10 larger x value LH 5 smaller x value 10 larger x value 10 10 5 y 10 10 10

Find the standard form of the equation of the hyperbola with the given characteristics Vertices 5 4 5 4 foci 5 9 5 9

25x 9y 225 a Find the standard form of the equation of the hyperbola If the hyperbola is degenerate enter NONE in each answer blank b Find the center vertices and foci of the hyperbola center x y vertices x y 1 x y foci x y x y 15 10 5 15 Find the asymptotes of the hyperbola Enter your answers as a comma separated list of equations 10 smaller x value c Sketch the hyperbola Use a graphing utility to verify your answer y 5 15 10 5 10 15 10 larger x value 151 smaller x value larger x value y 15 10 5 10 15 y 5 10

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 standard form of the equation of the hyperbola with the given characteristics Vertices 0 2 foci 0 14

Maria has recently inherited 8900 which she wants to deposit into an IRA account She has determined that her two best bets are an account that compounds semi annually at an annual rate of 4 Account 1 and an account that compounds daily at an annual rate of 3 4 Account 2 Step 1 of 2 Which account would pay Maria more interest