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Mathematics Questions and Answers January 5, 2018

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Solve the equation accurate to three decimal places. 5 ( 3 ^ ( x 8 ) = 1 2 8 x =

Evaluate the integral. 1 0 x 2 + 2 x dx

Set up a double integral that gives the area of the surface on the graph of f over the region R . f ( x , y ) = e - x s i n ( y ) R = { ( x , y ) : 0 x 7 , 0 y x } d y d x
Set up a double integral that gives the area of

Use implicit differentiation to find dy dx if e x e y + y 2 + x = e + 1 .

An irregularly shaped water container is 5 units deep. It has a flat bottom and cross - sectional areas A ( z ) = ( z 3 + 2 z + 1 5 ) 1 3 units ? 3 where z is the depth measured from the bottom and the cross - sections are taken by planes parallel to the bottom. Initially the container is full of water. Then the water is pumped out of the
An irregularly shaped water container is 5 units

Evaluate the following limits . If needed, enter oo for and - oo for - . ( a ) lim x 6 x 3 - 7 x 2 - 3 x 6 - 1 1 x - 1 0 x 3 = ( b ) lim x - 6 x 3 - 7 x 2 - 3 x 6 - 1 1 x - 1 0 x 3 =
Evaluate the following limits . If needed, enter

Electrical power P is given by P = E 2 R , where E is voltage and R is resistance. Approximate the maximum percent error in calculating power when 1 2 0 volts is applied to a 2 , 0 0 0 ohm resistor and the possible percent errors in measuring E and R are 2 % and 3 % , respectively. ( Round your answer to the nearest percent. ) d P P = %
Electrical power P is given by P = E 2 R , where

2 7 5 4 Evaluate the definite integral. 3 7 . yy 3 y 6 s 4 sec 2 yd dy

u varies inversely with the cube of p In your equation, use k as the constant of proportionality

\ int \ sqrt ( 2 - 5 s ) ds evaluate the integral

Find dy / dt . 1 0 ) y = ( 1 + sin 1 2 t ) - 4 A ) - 4 8 ( 1 + sin 1 2 t ) - 5 cos 1 2 t B ) - 4 8 ( cos 1 2 t ) - 5 C ) - 4 ( 1 + sin 1 2 t ) - 5 cos 1 2 t D ) - 4 ( 1 + sin 1 2 t ) - 5

( 3 3 + x 7 ) d x Evaluate

find the following limit lim ( x - > 0 ) ( ( - 1 ) / ( x ^ ( 2 ) ) )

Determine the equation of the parabola y = x ^ ( 2 ) + px + q ( i . e . determine coefficients p and q ) if it crosses X - axis at 2 and Y - axis at 4 .

The half - life of Radium - 2 2 6 is 1 5 9 0 years. If a sample contains 4 0 0 mg , how many mg will remain after 3 0 0 0 years?

Consider the curve C defined by y = f ( x ) = c o s ( x ) 2 - s i n ( x ) for 0 x 2 . It can be shown that y ' ( x ) = 1 - 2 s i n ( x ) ( 2 - s i n ( x ) ) 2 Hence, y ' ( x ) = 0 , when x = 6 . Find the minimum and maximum values of y , and the points where these occur, for 0 x 2 .
Consider the curve C defined by y = f ( x ) = c o

Find antiderivative 8 x ^ 3 - 6 x ^ 2 + 4 dx

( 1 , 3 ) ( i ) Find polar coordinates ( r , ) of the point, where r > 0 and 0 < 2 . ( r , ) = 1 0 , tan 1 ( 3 ) ( ii ) Find polar coordinates ( r , ) of the point, where r < 0 and 0 < 2 . ( r , ) = 1 0 , 2 tan 1 ( 3 )

Find the derivative of the given expression. f ( x ) = ln ( 4 x 2 1 5 x ) 1 7 x 4 f ( x ) = ln ( 4 x 2 1 5 x ) 1 7 x 4

The aranh of f is given below Use the graph to evaluate each definite integral. 0 4 | f ( x ) | d x = 6 2 - 2 f ( x ) d x = - 6 2 f ( x ) d x = - 6 4 f ( x ) d x = 2 2 - 9 f ( x ) d x = 2 6 [ f ( x ) + 4 ] d x = 6 0 - 7 f ( x ) d x = 5 6 f ( x ) d x =
The aranh of f is given below Use the graph to

P 4 . Find the second directional derivative f ( x , y ) = x e 2 y in the direction of v = 3 i + 4 j
P 4 . Find the second directional derivative f (

When a is positive, the series above is an alternating series. ( a ) Approximate 0 1 e - 1 2 x 2 d x to four decimal places accuracy by using the Alternating Series Test and its remainder theorem. ( Be careful to not round intermediate steps. ) ( b ) Using the same number of terms as you used in your sum in part ( a ) , compute the midpoint
When a is positive, the series above is an

indefinite integral ( ln ( x ) ) ^ 3 / xdx

( 2 ) The number N ( t ) of people in a community of 5 0 , 0 0 0 people who are exposed to a particular television advertisement for the first time can be modeled by a logistic equation. Find a model for d N d t that would model the rate at which the number of people see the first time as it is proportional to the number of people who have and
( 2 ) The number N ( t ) of people in a community

Using maclen series explantion find : lim when x goes to 0 c o s ( x 2 ) - 1 + 0 . 5 x 4 x 8

Determine the limit of the sequence defined below.an = 5 sin ( 3 n )

Given f ( x , y ) = e x s i n y a . Find an equation for the tangent plane at ( x , y ) = ( 3 , 2 ) . What direction should you move in from that point for the rate of change to be zero? c . Find the directional derivative at that point in the direction u = 3 i + 4 j
Given f ( x , y ) = e x s i n y a . Find an

If a straight line passes through the point x = 2 4 and y = 8 and also through the point x = 8 and y = 1 6 , the slope of this line is

Condense the expression 3 lnx 4 lny 3 \ ln x - 4 \ ln y 3 lnx 4 lny to a single logarithm.

Is the function c ( x ) = x ^ ( 2 ) - 8 x even, odd, or neither? even odd neither

Select the correct integration of the following function: dy / dx = 2 / x ? Select one: a . ( - 1 / 3 ) / x + c b . ( - 1 / 3 ) / x 6 + c c . ( 1 / 3 ) / x 6 + c O d . ( 1 / 3 ) / x 8 + c

Use the Laplace transform to solve the initial value problem y ' ' + 4 y = 1 + ( t - 4 ) , y ( 0 ) = 0 , y ' ( 0 ) = 6 ( use u ( t - c ) for the step function. ) y ( t )
Use the Laplace transform to solve the initial

let f ( x ) = arctan sqrt ( 1 + x / 1 - x ) , find df / dx and simplify

Determine the area that is bounded by the following curve and the x - axis on the interval below. ( Round your answer to three decimal places. ) y = x 2 - 4 , - 5 x 1 Viewing Saved Work Revert to Last Response
Determine the area that is bounded by the

Evaluate the definite integral below. 1 3 6 xe ( x 2 + 5 ) dx

This is similar to Section 3 . 7 Problem 1 2 : For the function f ( x ) = 3 x 2 + 3 x + ( 5 ) , determine the absolute maximum and minimum values on the interval [ 0 , 4 ] . Answer: Absolute maximum = at x = . Absolute minimum = at x = .

nd Present Value Question 2 , * 5 . 2 . 1 1 HW Score: 0 % , 0 of 1 4 poir Points: 0 of 1 Find the accumulated future value of the continuous income stream at rate R ( t ) , for the given time T , and interest rate k , compounded continuously. R ( t ) = $ 4 0 0 , 0 0 0 , T = 2 4 years, k = 6 % The accumulated future value is $ ( Round to the
nd Present Value Question 2 , * 5 . 2 . 1 1 HW

Engineering Mathematics 1 ( MAU 1 1 E 0 1 ) Homework 2 This is part of your continuous assessment and contributes to your final grade. Due date: Thursday, Dec 5 th 2 0 2 4 at midnight. No late assignments! Upload your ( scanned ) solutions to Blackboard as a single pdf file. No other formats! WRITE CLEAR AND CONCISE. SCRIBBLED SOLUTIONS WILL NOT
Engineering Mathematics 1 ( MAU 1 1 E 0 1 )

A manufacturer estimates that she can sell a maximum of 5 5 thousand cell phones in a city. By advertising heavily, her total sales grow at a rate proportional to the distance below this upper limit . If she enters a new market, and after 5 months her total sales are 1 2 thousand phones, find a formula for the total sales ( in thousands ) t months
A manufacturer estimates that she can sell a

Find general antiderivative of f ( x ) = \ sqrt ( x ) ( 3 + 1 0 x )

Given vec ( F ) = ( : 5 y z , 5 x z + 3 , 5 x y + 2 z : ) , find a function f so that vec ( F ) = gradf f ( x , y , z ) = + K Use your answer to evaluate C vec ( F ) * d v e c ( r ) along the curve C: x = t 2 , y = t + 5 , z = 3 t - 5 , 0 t 3
Given vec ( F ) = ( : 5 y z , 5 x z + 3 , 5 x y +

Find an exponential function that passes through the points ( 2 , 3 ) and ( 5 , 9 )

Given F ( x ) below, find F ( x ) . F ( x ) = 4 x 2 1 t 2 t + 5 dt

evaluando z z d S donde ( ) = { x , y , z x 2 + y 2 = z 2 ; - 1 z 0 } .

i got it wrong, i cant add the exponent and the . after the 1 0 ^ 5

A stone is dropped from the upper observation deck of a tower, 9 5 0 m above the ground. ( Assume \ ( g = 9 . 8 \ mathrm { ~m } / \ mathrm { s } ^ { 2 } \ ) . ) ( a ) Find the distance ( in meters ) of the stone above ground at time \ ( t \ ) . \ [ s ( t ) = \ ] ( b ) How long does it take the stone to reach the ground? ( Round your answer to two
A stone is dropped from the upper observation

( 8 ) The population of a town grows at a rate proportional to the population present at time t . If the population triples every 6 0 years ; how often does it take for the population to double?
( 8 ) The population of a town grows at a rate

Find the area of the region between the graphs of y = 1 1 - x 2 and y = - 5 x - 3 over the interval 3 x 1 0 . The area is
Find the area of the region between the graphs of

Your task is to write a report on finding a certain "area under the curve" for a function given a specific interval. Your report must introduce the function and explain what it is that you are trying to find by approximating the area under the curve ( introduction / objective ) , how you would find it ( methodology ) , provide a detailed
Your task is to write a report on finding a

Integrate: - 1 6 x 3 + 4 8 x 2 - 2 4 x + 7 7 1 6 x 2 + 2 5 dx

indefinite integral of e ^ ( 2 x ) ( 1 + e ^ ( 2 x ) ) dx

Find dy over dx if y equals 2 divided by the quantity x cubed period

For a smooth curve C represented by the parametric equations x = x ( t ) , y = y ( t ) , a t b , the arc length s satisfies the equation d s d t = ( d x d t ) 2 + ( d y d t ) 2 2 In terms of differentials, this can be written as d s = ( d x ) 2 + ( d y ) 2 2 The differential d s can be used to approximate the arc length s between two nearby
For a smooth curve C represented by the

Evaluate the integral below. - 2 c o s 3 ( 4 x ) s i n 3 ( 4 x ) d x Be sure to put the argument of the trigonometric functions in parentheses.
Evaluate the integral below. - 2 c o s 3 ( 4 x )

[ 2 pts each ] The graph of a function f is shown. Find each of the items below. In some cases, you will need to estimate. It may help to show markings on the graph to show how you estimated. If either of the symbols or - applies, use it . If an item does not exist and neither of these symbols applies, write "DNE." ( a ) lim x 1 f ( x ) q , ( b )
[ 2 pts each ] The graph of a function f is

The tank is half full of oil with a density of 5 0 pounds per cubic foot. How much work is done in pumping the oil out over the top of the tank? Round to the nearest whole number. [ ? ] foot - pounds
The tank is half full of oil with a density of 5

A cylindrical tank is 6 feet tall and has a radius of 1 foot. The water is being drained from the tank at a rate of 1 0 cubic feet per minute. How fast is the water level in the tank dropping when the water level in the tank is 4 feet high ? Note: The volume of a cylinder is given by the formul V = r 2 h . [ A ] 4 feet per minute [ B ] 5 2 feet
A cylindrical tank is 6 feet tall and has a

Calculate 0 sin ( 1 . 9 1 t ) dt 0 sin ( 1 . 9 1 t ) dt

To find the velocity at a general time t = a , we need to first simplify the limit as much as possible. v ( a ) = lim h 0 7 ( a + h ) 2 7 a 2 h = lim h 0 7 a 2 7 2 a 2 ( a + h ) 2 h = lim h 0 7 a 2 7 a 2 + + h 2 ha 2 ( a + h ) 2 = lim h 0 h ha 2 ( a + h ) 2 = lim h 0 a 2 ( a + h ) 2

If you paid $ 4 0 to a loan company for the use of $ 1 , 6 6 1 for 7 3 days, what annual rate of interest did they charge? ( Assume a 3 6 0 - day year. ) The annual rate of interest is

The demand equation for your company's virtual reality video headsets is p = 1 , 0 0 0 q 0 . 3 , where q is the total number of headsets that your company can sell in a week at a price of p dollars. The total manufacturing and shipping cost amounts to $ 8 0 per headset. ( a ) Find the function P for weekly profit, in millions of dollars and in

Directions: Calculate the following definite integral. 0 4 s i n x l n ( c o s x ) d x =
Directions: Calculate the following definite

Select the correct slope and y - intercept for the following linear equation: y = 4 x - 5 slope = - 5 y - intercept = ( 0 , 4 ) slope = 4 y - intercept = ( - 5 , 0 ) slope = - 5 y - intercept = ( 4 , 0 ) slope = 4 y - intercept = ( 0 , - 5 )
Select the correct slope and y - intercept for

2 0 . Use the following graph of \ ( f ( x ) \ ) to Illustrate \ & Analyze the Mean Value Theorem for Integrals on the interval \ ( [ - 4 , 1 ] \ ) ( all scale markings are units of 1 ) .
2 0 . Use the following graph of \ ( f ( x ) \ )

Find the limit of the following sequence. If the limit does not exis a n = 3 + 5 n 2 n + n 2
Find the limit of the following sequence. If the

If the perimeter of a rectangle is 7 x ^ ( 4 ) - 8 x ^ ( 3 ) + 1 2 x - 9 , and the length is x ^ ( 2 ) - 4 x + 3 , find the width.

write the equation of f ( x ) = x ^ ( 2 ) that has been reflected over the x - axis, vertically stretched by a factor of 3 , shifted right 5 , and shifted down 8 f ( x ) = x ^ ( 2 )

Find a general solution of the following first order linear differential equation dy / dx

Evaluate the integral. ( Remember the constant of integration. ) x 5 e 2 4 x 6 dx

Evaluate 6 1 1 ( t 2 1 ) ( t 2 4 ) dt using the Fundamental Theorem of Calculus, Part 2 . Enter only exact answers.

Evaluate: 2 1 0 1 3 x + 2 d x
Evaluate: 2 1 0 1 3 x + 2 d x

The differential equation d / dx ( y ) = 0 . 2 5 y ^ 2 is to be solved using the backward ( implicit ) Euler's method condition y = 1 at x = 0 and with the a step size of 1 What would be the value of y at x = 1 ? ( A ) 1 . 3 3 ( B ) 1 . 6 7 ( C ) 2 . 0 0 ( D ) 2 . 3 3

Find. 3 x 2 e 2 x 3 d x A . 3 e 2 x 3 + C B . 1 6 e 2 x 2 + C C . 1 2 x 2 e 2 x 3 + C D . 1 2 e 2 x 3 + C Option D Option A Option C Option B
Find. 3 x 2 e 2 x 3 d x A . 3 e 2 x 3 + C B . 1 6

Evaluate the following. Copy down each problem. Simplify your answers. On # 2 and # 4 , show your work, use proper notation, and keep things organized. Hint: # 1 and # 3 should help you with # 2 and # 4 . d d x ( 1 2 x 2 + 3 ) - 1 3 - 2 4 x ( x 2 + 3 ) 2 d x d d x ( 1 2 l n ( x 2 + 3 ) ) - 1 3 2 4 x x 2 + 3 d x
Evaluate the following. Copy down each problem.

Find the following limit or state that it does not exist. ModifyingBelow lim With x right arrow minus 1 limx 1 ( - 2 x + 3 )

The percentage of P Doctors who accept a new medicine is given by P ( t ) = 1 0 0 ( 1 - e ^ ( - 0 . 2 1 t ) ) , where t = time in months. Find P ' ( 7 )

It is common to think of 7 2 = 9 . 8 7 approximation, as 1 0 . 0 0 . What are the absolute and relative errors in this approximation?

Consider the problem of evaluating the definite integral: 0 1 4 - x 2 2 d x = ? ( a ) Give the substitution which is used to solve this problem. ( b ) Give the new limits of integration after the substitution is made. c ) Give the numerical answer for the problem.
Consider the problem of evaluating the definite

Evaluate the definite integral S 2 0 ( 2 e ^ x ) using the fundamental Theorem. then evaluate the same integral approximately

We should compare a n = 5 n ( n + 1 ) 3 with the sequence: b n = 1 n 3 b n = 1 n 2 b n = 1 n b n = n b n = n 2 And now we evaluate: lim n a n b n =
We should compare a n = 5 n ( n + 1 ) 3 with the

Choose the series that diverges by the Divergence - term
Choose the series that diverges by the Divergence

Alexis sells her business and receives yearly payments on a sliding seale according to the function P ( t ) = 4 2 0 0 0 - 4 0 0 0 t , fot 0 t 8 . It this is treated as a continuous income stream and deposited into an account that earns 4 . 4 8 % compounded continuously, how much will Alexis's account be worth after 8 years: ( Round your answer to
Alexis sells her business and receives yearly

Evaluate I = C ( s i n x + 8 y ) d x + ( 8 x + y ) d y for the nonclosed path ABCD in the figure. A = ( 0 , 0 ) , B = ( 1 , 1 ) , C = ( 1 , 2 ) , D = ( 0 , 3 )
Evaluate I = C ( s i n x + 8 y ) d x + ( 8 x + y

Question 3 ( 3 points ) ( 3 pts ) The table shows the velocity of a bicyclist riding for 3 0 seconds. Use the Riemann sum with right - endpoint values to estimate the distance using 6 intervals of length 5 . \ table [ [ Time ( s e c ) , 0 , 5 , 1 0 , 1 5 , 2 0 , 2 5 , 3 0 ] , [ Velocity ( ft / sec ) , 0 , 6 , 1 2 , 1 8 , 2 6 , 2 4 , 2 2 ] ] Done
Question 3 ( 3 points ) ( 3 pts ) The table shows

The sum of the two - power series n = 2 3 n c n x n - 1 + n = 0 4 c n x n + 1 is given as: k = 1 [ 4 ( k + 1 ) c k + 1 + 3 c k - 1 ] x k the above option k = 1 [ 3 ( k + 1 ) c k + 1 + 4 c k - 1 ] x k the above option None of the mentioned
The sum of the two - power series n = 2 3 n c n x

Evaluate the following integral. 6 1 6 0 ( 2 x 2 + y 2 ) dxdy

COMPARING METHODS Find the inverse of the function f ( x ) = - 3 x + 4 by switching the roles of x and y and solving for y . Then find the inverse of the function f by using inverse operations in the reverse order. Which method do you prefer? Explain.

. ( 1 0 points ) . Evaluate the double integral D 2 xydA, D = { ( x , y ) | 0 y 1 , y 2 x y }
. ( 1 0 points ) . Evaluate the double integral D

Can someone show me how to answer this step by step? Assume that C ( x ) is in dollars and x is the number of units produced and sold. For the total - cost function C ( x ) = 0 . 0 1 x ^ ( 2 ) + 0 . 6 x + 2 0 , find \ Delta C and C ^ ( ' ) ( x ) when x = 6 0 and \ Delta x = 1 . \ Delta C = $ ( Simplify your answer. Type an integer or decimal
Can someone show me how to answer this step by

Find the tangent plane to the surface that contains the curves vec ( r ) 1 ( t ) = ( : t , t 2 , - 1 : ) and vec ( r ) 2 ( t ) = ( : t 3 , 1 , t : ) at the point ( - 1 , 1 , - 1 ) . ( a ) - x + y - z = 0 ( b ) 2 ( x + 1 ) - ( y - 1 ) + 6 ( z + 1 ) = 0 ( c ) 2 ( x + 1 ) + ( y - 1 ) - 6 ( z + 1 ) = 0 ( d ) Not enough information
Find the tangent plane to the surface that

Solve the riven DEs by undetermined coefficients. xy ' ' + y ' = 0 x 2 y ' ' + xy ' + 4 y = 0

A sequence satisfies the recurrence relation yk + 2 = 3 yk 2 yx + 1 with y 0 = 1 and y 1 = 1 . Write out the next five terms ( k = 2 to k = 6 ) of this sequence.

In a certain city the temperature ( in F ) t hours after 9 a . m . was modeled by the function T ( t ) = 5 0 + 1 9 sin t 1 2 . Find the average temperature Tave ( in F ) during the period from 9 a . m . to 9 p . m . ( Round your answer to the nearest degree. )

Identify the intervals of concavity for g ( t ) = 4 t ^ ( 4 ) - 1 0 t ^ ( 3 ) + 7 t - 4 . ( Separate multiple intervals with commas. Enter exact values using fractions. ) Concave Down: Concave Up:
Identify the intervals of concavity for g ( t ) =

Evaluate the integral by making the given substitution. ( Use C for the constant of integration. ) x 2 x 3 + 1 2 d x , u = x 3 + 1
Evaluate the integral by making the given

what function represents the relationship between x any when y is ( 7 ) / ( 3 ) and x is 2 1

write down a primative of the following functions f ( x ) = sqrt ( x ^ 2 - 9 ) for x in ( 3 , infinity )

Write a formula for the inverse of the function y = 5 ( 1 0 ) ^ x

Find all values of x where the slope of the tangent line tof ( x ) = 4 x 2 + 5 x + 5 is 0 .

Find the absolute extrema if they exist, as well as all values of x where they occur, for the function f left parenthesis x right parenthesisf ( x ) equals = x cubed plus 6 x squared plus 9 x minus 8 x 3 + 6 x 2 + 9 x 8 on the domain left bracket negative 5 comma 0 right bracket [ 5 , 0 ] . Question content area bottom Part 1 Identify the absolute

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