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mathematics
may 2018
22

Mathematics Questions and Answers May 22, 2018

Expert-verified solutions to help you succeed

Determine whether the algebraic expression is is a polynomial, state the degree. 4 p ^ ( 3 ) n ^ ( 5 ) - 3 p ^ ( 2 ) n ^ ( 4 ) + 4 p ^ ( 4 ) n ^ ( 2 ) - 2 pn ^ ( 4 ) + 4 p ^ ( 4 ) n ^ ( 4 )

Find the limit . limx 8 7 8 3

Find an exact solution for ln ( 7 ) + ln ( 7 x 2 3 ) = ln ( 1 0 0 )

The growth of bacteria in a dish is modeled by the function f ( t ) = 2 ^ ( ( 1 ) / ( 3 ) ) . For which value of t is f ( t ) = 3 2 ? A . 8 B . 2 C . 1 5 D . 1 6

\ int _ ( - 3 ) ^ 3 ( 3 - | x | ) dx

Evaluate the following limit . Enter the exact answer. To enter a a , type sqrt ( a ) . limx 0 x + 5 5 x = limx 0 x + 5 5 x =

How to determine the centroid of an area between y = x and y = x ^ 3 / 9

Find the equation of the line with slope = - 5 and passing through ( 8 , - 3 ) . Write your equation in point - slope AND slope - intercept forms. point slope form

Find all numbers for which the rational expression is undefined. - ( 1 5 ) / ( 1 6 x )

Question 6 Solve for w . - ( 3 ) / ( 8 ) w = 1 8 Simplify your answer as much as possible.

Find the product and write the result in standa ( 2 - 8 i ) ( - 6 - 3 i )

for what values of x is x ^ 6 greater than or equal to x ^ 8 ? for what values is x ^ 6 less than or equal to x ^ 8 ?

Let f ( x ) = { | x | x 2 a 2 x aif x < 1 , if x > 1 . f ( x ) = { | x | if x < 1 , x 2 a 2 x aif x > 1 . If limx 1 f ( x ) limx 1 f ( x ) exists, what must be the value of aa ? a =

evaluate the limit lim x - > - 1 ( x ^ 2 - 7 x - 8 ) / x + 1

Assume that f is a one - to - one function. ( a ) If f ( 4 ) = 1 6 , find f 1 ( 1 6 ) . f 1 ( 1 6 ) = ( b ) If f 1 ( 9 0 ) = 4 5 , find f ( 4 5 ) . f ( 4 5 ) =

QUESTION 1 What is the general form of a seperable differential equation? A . d y d x = f ( x ) B . d y d x = f ( y ) C . d y d x = f ( x ) g ( y ) D . d y d x = f ( x ) + g ( y ) E . none of the answer choices

Q - 5 ) Use the following data to find the velocity and acceleration at t = 5 seconds a ) Derive the first backward differentiation formula for the second derivative of function \ ( f \ ) . b ) Calculate the velocity and acceleration at \ ( t = 5 \ ) seconds using the first central differentiation formula approximately. c ) Calculate the velocity

Simplify. ( z ^ ( - 9 ) ) / ( z ^ ( - 3 ) ) Write your answer with a positive exponent only.

Simplify ( - b ) / ( 2 a ) where a = 8 and b = 7 Write your answer as a reduced fraction.

Sketch graphs by hand and use them to make approximations for each of the limits in Exercises 5 3 - 6 6 . If a two - sided limit does not exist, describe the one - sided limits . 5 3 . lim x 0 1 x 5 5 . lim x 1 x 2 - 1 x - 1 5 7 . lim x 1 x - 1 x 2 - 1 5 9 . lim x ( 1 - e - x )

Exercise 1 . 2 . 1 5 Show that a z + b y + c z = 0 a 1 x + b 1 y + c 1 z = 0 always has a solution other than x = 0 , y = 0 , z = 0 .

Question 2 Differentiate f ( u ) = 0 . 0 7 u 4 - 1 . 2 1 u 3 3 u - f ' ( u ) = 2 . 8 u 3 - 3 . 6 3 u 2 3 f ' ( u ) = 4 u 3 - 3 u 2 3 f ' ( u ) = . 4 u 3 - 3 u 2 3 f ' ( u ) = . 2 8 u 3 - 3 . 6 3 u 2 3

what is the rate of change for the function y = x ^ 2

aniderivative of - 8 e ^ - 8 x

1 1 . For the differential equation x ' = x ^ 3 , ( a ) Show that x ( t ) = sqrt ( 1 / ( C - 2 t ) ) ( b ) Find one solution of x ' = x ^ 3 that cannot be written in this form for any value of C . ( c ) Find the solution satisfying the initial condition x ( 0 ) = 1 , and sketch its graph. ( d ) Does the solution in part ( c ) have a vertical

limx 2 limx 2 | x 2 | x 2 x - 2 x - 2 = _ _ _ _ _ _ _ _

Limits at Infinity at Use the link below to explore limits at infinity. As x heads to either positive or negative infinity, how are the y - values behaving? Are they heading to positive or negative infinity or to a constant value? List each function and describe its end behavior from the given function graphs. For each of the functions below,

Write the equation you get when you start with y = x 2 and do vertical stretch of 3 , a horizontal reflection, translations of 2 right and 4 up .

The following is the graph of f ( x ) = sec ^ 2 ( x ) + 5 and the line y = 7 . a . Setup an integral representing the area of the shaded region. Take advantage of symmetry, if possible.

Write the equation of the horizontal line passing through the point ( negative 5 , 2 ) .

a rock is thrown upward with a velocity of 3 5 meters per second. its height meters seconds later is given by the function h ( t ) = 3 5 t - 4 . 9 t ^ 2 determine the average velocity of the rock over the time interval [ 3 , 3 . 1 ] determine the average velocity of the rock over the time interval [ 3 , 3 . 0 1 ] determine the average velocity of

Evaluate the following expression. limx 2 3 x 2 + 4 x Select the correct answer below: 2 0 - 4 - 2 0 2

evaluate the integral ( 1 - tan ^ 3 x ) / ( sec ^ 2 x ) dx

Evaluate the integral. 2 y + 6 y 8 y 3 dy 1

Question 1 A massage therapy office offers hourly massage sessions to the public. The office has fixed overhead costs totaling of \ ( \ $ 3 7 8 4 \ ) per month and pays their massage therapists an hourly rate of \ ( \ $ 7 4 \ ) per hour. If the company can charge clients \ ( \ $ 1 1 8 \ ) per hour, find the Cost Function \ ( \ mathrm { C } ( \

For the function g whose graph is given, state the value of each quantity, if it exists. ( If an answer does not exist, enter DNE. ) q , ( a ) lim t 0 - g ( t ) [ ( b ) lim t 0 + g ( t ) ( c ) lim t n g ( t ) ( d ) lim t 2 - g ( t ) ( e ) lim + - 0 + g ( t ) ( f ) lim x - g ( t ) ( g ) g ( 2 ) ( h ) lim h 1 g ( t )

find the derivative using the ftoc integral of 1 to sqrt x: sqrt t ^ 4 + 6

The letters a and b represent nonzero constants. Solve ax + b = 5 8 for x .

Alex deposits $ 7 0 0 0 into an account that erns 2 . 9 5 % per year, compounded continuously. The value of their account after t years is given by P ( t ) = 7 0 0 0 e ^ ( 0 . 0 2 9 5 ) t . Calculate the rate at whcih the total amount is increasing in alex's account in 4 years.

Parte I: Utilice una integral iterada para hallar el rea de la regi n: Tomado de: C lculo 2 de varias variables, 9 ed , Larson & Edwards Tomado de: C lculo 2 de varias variables, 9 ed , Larson & Edwards

How to solve Between 2 0 0 6 and 2 0 1 6 , the number of applications for patents, N , grew by about 3 . 6 % per year. That is , N ' ( t ) = 0 . 0 3 6 N ( t ) . a ) Find the function that satisfies this equation. Assume that t = 0 corresponds to 2 0 0 6 , when approximately 4 5 5 , 0 0 0 patent applications were received. b ) Estimate the number

Consider a real - valued function f as defined below: f ( x ) = ( x - 2 ) 2 + 5 + k For what values of k would the graph of f would neither touch nor intersect the x - axis? k > - 5 k 0 k - 5 No such k values exis k - 5

Find f ' ( x ) for the function f ( x ) = 4 x 2 by using the definition of the derivative, given below. Note: Failure to use the definition of the derivative and failure to show all steps and work will result in zero points for this question. lim h 0 f ( x + h ) - f ( x ) h

Find all local extra values and saddle points f ( x , y ) = 9 ^ 3 + y ^ 3 / 3 - 4 xy

An accessories company finds that the revenue, in dollars, from the sale of x belts is given by R ( x ) = 6 5 x 9 1 0 . Find the rate at which average revenue is changing when 1 8 0 belts have been produced and sold. First, find the rate at which the average revenue is changing when x belts have been produced. ? b a r ( R ) ' ( x ) = When 1 8 0

Consider the following. f ( x , y , z ) = x s i n ( y z ) ( a ) Find the gradient of f . ( b ) Find the directional derivative of f at ( 3 , 4 , 0 ) in the direction of v = i + 4 j - k . ] ( b ) At ( 3 , 4 , 0 ) we have gradf ( 3 , 4 , 0 ) = . The unit vector in the direction of v = i + 4 j - k is u = Therefore the equation D u f ( x , y , z ) =

Find the components of the vectors. \ [ \ langle i \ ]
$Find the components of the vectors. \ [ \ langle$

Given the function f , evaluate f ( 3 ) , f ( 2 ) , f ( 1 ) , and f ( 0 ) . f ( x ) = 2 x ^ 2 + 9 if x 1 . 3 x 1 0 if x > 1

which best represents the soultion set of the inequality | 2 x + 5 | > 7 ?

A force of 6 N is required to stretch a spring of natural length of 1 . 2 5 m to a length of 1 . 5 m . Find the work done in stretching the spring from its natural length to a length of 2 m . Remember that = 0 when the spring is its natural length

the position of a particle at time t is s ( t ) = 5 t ^ 3

Evaluate the expression. 4 ^ 2 + 1 2 2

Find the limit . ( If an answer does not exist, enter DNE. ) lim x 7 x 1 / 2 x + 6

Solve for w in the following equation for perimeter of a rectangle: P = 2 l + 2 w

6 True or False 1 point ( - 1 , - 1 ) is a solution to the following system of linear equation y = 4 x + 3 y = - x - 2 True False

Determine the slope function S ( x ) for the following function. f left parenthesis x right parenthesis equals StartAbsoluteValue 5 . 5 x EndAbsoluteValuef ( x ) = 5 . 5 x

/ 2 0 0 0 Solution Question 1 4 of 2 0 Find the area A of the part of the circle r = 1 1 s i n ( ) + 1 1 c o s ( ) in the fourth quadrant. ( Use symbolic notation and fractions where needed. )

Find the limit . lim x e 8 x cos ( x )

Write a definite integral that yields the area of the region. ( Do not evaluate the integral. ) f ( x ) = 8 ( i )

lem 7 : ( 4 points ) ( a ) Given the function f below, evaluate 1 1 6 f ( x ) d x . f ( x ) = { x 3 - 2 x , x 4 x 2 - 2 x , 4 x 1 0 x - 3 x 2 , x 1 0

Find the equation of the parabola with a directrix of x = 2 and a focus of ( 4 , 4 )

Step 1 of 4 : Find lim x - 4 - f ( x ) . 2 Points 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.

Question 7 Completely simplify y = - 2 x ^ ( 3 ) ( x + 4 ) ^ ( 2 ) . You must show all of your work to receive credit.

Find the derivative of the function. r = ( 1 + 3 0 / 3 0 ) * ( 3 - 0 )

determine the slopes of the line passing through the given points ( 3 , - 1 / 7 ) and ( 4 , 8 / 9 )

twice a number added to another number is - 8 . The differnce of the two numbers is 2 . Find the number

This is similar to Section 2 . 2 Problem 2 8 : Use algebraic simplifications to find the limit . Use a fraction.

Parte II: rea de Superficie Hallar el rea de la superficie dada por z = f ( x , y ) sobre la regi n R . f ( x , y ) = 1 2 + 2 x - 3 y ; R = { ( x , y ) : x 2 + y 2 9 f ( x , y ) = 9 - x 2 R cuadrado cuyos v rtices son ( 0 , 0 ) , ( 2 , 0 ) , ( 0 , 2 ) , ( 2 , 2 )

Math 1 7 6 Worksheet # 3 ( Sec . 1 . 4 Differentiation Using Limits of Difference Quotients and Sec. 1 . 5 Differentiation Techniques: The Power and Sum - Difference Rules ) Directions: You may work with others. Use complete sentences when asked to give an explanation. Show all your work. 1 . ) Suppose f ( x ) = x 2 4 x - 9 . a . ) Find f ' ( x )

Evaluate the integral. / 2 8 cos 5 ( x ) dx

A graphing calculator is recommended. Use a graph to find a number such that if | x - 2 | 8 , then | x 2 + 5 2 - 3 | 0 . 2 ( Round your answer down to three decimal places. ) = Need Help?

1 Jackie simplified the expression ( 3 x + 1 ) ( x - 3 ) - ( 2 - 2 x ^ ( 2 ) - 3 x ) 4 The What is the constant term in the simplified expression? A - 5 B - 1 C 1 D 5

Find the average rate of change of f ( x ) = 1 x 2 on the interval - 1 , 1 . Answer in fraction form.

Find the location and value of all relative extrema for the function. A ) Relative maximum of 0 at 0 ; Relative minimum of 3 at - 2 ; Relative minimum of 0 at 6 . B ) Relative maximum of 0 at 0 ; Relative maximum of 0 at 6 . C ) Relative minimum of - 2 at 3 ; Relative maximum of 0 at 6 . D ) Relative minimum of - 2 at 3 .

Determine whether the given CT system is linear or not. y ( t ) = x s i n ( t ) y ( t ) = s i n x ( t ) y ( t ) = t 2 2 x ( t - 1 ) y ( t ) = e x ( t ) Answers: 1 . Linear 2 . Nonlinear 3 . Linear 4 . Nonlinear

find the second derivative of g ( x ) = 7 x 3 + 1 x 2 g ( x ) = 7 x ^ 3 + \ frac { 1 } { x ^ 2 } g ( x ) = 7 x 3 + x 2 1 .

Sketch the graph of the function. ( If an answer does not exist, enter DNE. Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response. ) f ( x , y ) = s i n ( x ) ( Write an equation for the cross section at y = - 2 using x and z . ) ( Write an equation for the cross section at y = 0 using x

Limit as n approaches infinity of An = ( 1 + 4 / n ) ^ n

Determine whether the given equation is linear. 3 x ^ ( 2 ) - 4 = 1 4 Is the equation linear or nonlinear? Linear Nonlinear

Determine the order of the following differential equation. y + 6 y = 9 y ^ 4

For a differential equation of order n , how many initial conditions do we need?

What are the positive and negative square roots of 1 0 , 0 0 0 ? and Submit

Let f ( t ) be a function on [ 0 , infinity ) . The Laplace transform of f is the function F defined by the integral F ( s ) equals = Integral from 0 to infinity e Superscript negative st Baseline f left parenthesis t right parenthesis dt 0 e stf ( t ) dt . Use this definition to determine the Laplace transform of the following function. f ( t )

Given f ( x ) = x 4 2 , apply the three conditions from the definition of continuity to determine where an interval, if one exists, where the function is continuous. State why each of the 3 condition holds on the interval.

Consider the following. 4 0 ( x 2 2 x ) dx Consider the following theorem. If f is integrable on [ a , b ] , then bf ( x ) dxa = lim n nf ( xi ) xi = 1 , where x = b an and xi = a + i x . Use this to evaluate the integral.

0 5 2 [ x ] d x is ( a ) 2 5 2 ( b ) 2 5 2 - 1 ( c ) 2 5 2 - 2 ( d ) 2 5 2 - 3

Evaluate the integral. 8 x cos ( 3 x ) dx

omework Use the power rule and the power of a product r ( 3 p ^ ( 9 ) ) ^ ( 4 )

Use Lagrange multipliers to find the shortest distance from the point ( 7 , 1 0 , 8 ) to the plane 9 x + 8 y - 3 z = 7 . 1 1 2 8 1 5 4 2 7 1 5 4 2 8 1 5 4 2 1 1 1 1 1 5 4 2 8

Boat A cruises northwest at a rate of 1 6 knots ( nautical miles per hour ) . Boat B cruises north at a rate of 2 0 knots. assume that x - axis points to the east and y - axis points to the north. a ) find the displacement vector from boat a to boat b half an hour later. ai + bj , where a = ? and b = ? equals b ) for the passengers in boat a ,

( 1 6 ( 1 . 0 1 ) - 1 . 8 6 ( 1 . 0 1 ) ^ 2 ) - ( 1 6 ( 1 ) - 1 . 8 6 ( 1 ) ^ 2 ) / . 0 1

Differentiate. y = square root x / ( square root x ) + 7 y =

Differentiate the function. y = 7 x ^ 1 / 2 + 5 x / 2 x ^ 2

Let f be the function defined by the equation below. f ( x ) = 8 x 2 Find the following. f ( 3 ) = f 1 4 = f ( 0 ) = f ( a ) = f ( a + 1 ) =

a paraglider reached a height of 8 , 4 0 0 ft after 4 hours the paraglider was at an elevation of 2 , 2 0 0 ft what is the change in elevation per hour?

Find the volume of the solid generated by revolving the shaded region about the \ ( y \ ) - axis. Find the volume of the solid generated by revolving the shaded region about the y - axis. The volume of the solid generated by revolving the | shaded region about the y - axis is ( Type an exact answer, using pi as needed. ) please help with a clear

If an initial amount of $ 2 2 0 0 is invested in an account at an annual interest rate of 4 . 9 % , compounded continuously, the total amount in the account after t years is given by: A ( t ) = 2 2 0 0 e ^ 0 . 0 4 9 t Find the rate of change of the total amount in the account after 4 years. ( Round the answer to the nearest cent ) . The total

Find two unit vectors orthogonal to a = ( : 3 , - 5 , 5 : ) and b = ( : 2 , 5 , - 2 : ) Enter your answer so that the first non - zero coordinate of the first vector is positive.

Find the following limit: lim x 6 x 2 - 1 2 x 2 + 7 x

code class = "asciimath" > At observation t , a consumer is observed to buy the bundle x ^ ( t ) inR _ ( + ) ^ ( l ) at prices p ^ ( t ) inR _ ( + + ) ^ ( l ) . Suppose we make the following three observations of a consumer: p ^ ( 1 ) = ( 2 , 2 , 2 ) , x ^ ( 1 ) = ( 2 , 0 , 2 ) ;p ^ ( 2 ) = ( 1 , 2 , 3 ) , x ^ ( 2 ) = ( ( 1 ) / ( 2 ) , 3 , ( 1 ) /
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