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mathematics
june 2018
18

Mathematics Questions and Answers June 18, 2018

Expert-verified solutions to help you succeed

The form o f the partial fraction decomposition o f a rational function i s given below. - ( 2 x 2 + 9 x + 4 5 ) ( x - 3 ) ( x 2 + 9 ) = A x - 3 + B x + C x 2 + 9 A = B = C = Now evaluate the indefinite integral. - ( 2 x 2 + 9 x + 4 5 ) ( x - 3 ) ( x 2 + 9 ) d x =
$The form o f the partial fraction decomposition o$

Consider the following repeating decimal 0 . 2 write the repeating decimal as a geometriu series n = 0 to infinity b ) write the sum of the series as the ratio of two integers

Calculate all of the critical points of the function: f ( x , y ) = x 6 + y 6 + 6 xyf ( x , y ) = x 6 + y 6 + 6 xy Enter the ordered triple with x and y both positive. is a Select an answer relative maximum relative minimum saddle point there are none . Enter the ordered triple with x and y both negative. is a Select an answer relative minimum

Find the derivative of the logarithmic function. y = ln x x 2 3 y ( x ) =

Find the indicated derivative. dydx for y = 1 2 x 2 x 4 2 x 2 + 3 dydx

QUESTION 5 - 1 POINT Find d d x ( - 2 x 4 x - 5 2 ) . Provide your answer below: d d x ( - 2 x 4 x - 5 2 ) =

Profit of a Vineyard Phillip, the proprietor of a vineyard, estimates that the first 9 9 0 0 bottles of wine produced this season will fetch a profit of $ 3 per bottle. However, the profit from each bottle beyond 9 9 0 0 drops by $ 0 . 0 0 0 1 for each additional bottle sold. Assuming at least 9 9 0 0 bottles of wine are produced and sold, what is

Devise an exponential decay function that fits the given data, then answer the accompanying question. Be sure to identify the reference point \ ( ( t = 0 ) \ ) and units of time. The homicide rate decreases at a rate of 5 \ % per year in a city that had 9 0 0 homicides / yr in 2 0 1 0 . At this rate, when will the homicide rate reach 7 0 0

differentiate g ( t ) = 9 t ^ 3 cos ( t )

Find the derivative of the function: g ( x ) = 7 a r c c o s ( x 4 )

Evaluate the integral. 1 4 8 + u 2 u 3 d u

Find the distance between the points using the following methods. ( 1 , 5 ) , ( 6 , 7 ) ( a ) the Distance Formula ( b ) integration

Question 1 2 of 2 1 Determine the one - sided limit numerically. ( Use decimal notation. Give your answer to three decimal places. ) lim x 0 - 4 s i n ( x ) 7 | x | =

Given the function f ( x ) = x 7 2 , calculate the following values. f ( 2 9 ) = f ( - 6 ) = f ( 4 2 ) = f ( 5 7 ) =

Evaluate the integral. 1 1 6 1 x 2 d x - 1 0 6 1 0 - 7

consider the region bounded by y = e ^ x , the axis, and the lines x = 0 and x = 3 . Find the volume of the solid whose base is the given rgion

Find the derivative of the logarithmic function. h ( x ) = ln ( 6 x 2 + 1 ) h ' ( x ) =

surface o f mountain h ( x , y ) = 7 5 0 0 - 0 . 0 0 1 x 2 - 0 . 0 0 4 y 2 . i f a mountain climber i s a t the point ( 3 0 0 , 5 0 0 , 6 4 1 0 ) . I n what direction should the climber move i n order t o ascend a t the greatest rate?

Find the limit , if it exists. ( 3 pts each ) Given lim x 5 f ( x ) = 4 and lim x 5 g ( x ) = - 5 , find lim x 5 2 f ( x ) 3 g ( x ) 3 f ( x ) .

Problem 4 : Compute the General Solution for: d 2 y d t 2 d y d t 6 y = e 3 t 3 t 2 Problem 4 : Compute the General Solution for: d 2 y d t 2 - d y d t - 6 y = e 3 t - 3 t 2

Use the function below and find f ' ( 4 ) . ( x ) = - 5 x 2 + 1 5 x

Find the length of the following curve. y = - x ^ 2 / 2 4 + 3 lnx , 6 lessthanorequalto x lessthanorequalto 3 6

Consider the following. lim x 2 2 x 2 5 x 1 8 x + 2 Find the limit of the function ( if it exists ) . ( If an answer does not exist, enter DNE. ) Write a simpler function g ( x ) that agrees with the given function at all but one point. g ( x ) =

Evaluate the definite integral of the algebraic function. 1 9 u - 8 u 2 d u

f we are asked to find the indefinite integral of sin ^ 5 xcos ^ 6 x , which identities can we use to simplify the integrand?

Find an explicit solution to xy = y 2 , y ( 1 ) = 1

What is the probability that a five - card poker hand contain a flush? ( i . e . five cards of the same suit )

The surface S consists o f the top and the four sides ( b u t not the bottom ) o f the cube with one corner a t ( - 2 , - 2 , - 2 ) and a diagonal corner a t ( 3 , 3 , 3 ) , with outward orientation. I f vec ( F ) ( x , y , x ) = ( : x y z , x y , x 2 y z : ) then: S curl ( v e c ( F ) ) * d v e c ( S ) = ( S u g g e s t i o n : Use the Curl

Provide a n appropriate response. The curve y = a x 2 + b x + c passes through the point ( 2 , 2 8 ) and i s tangent t o the line y = 4 x a t the origin. Find a , b , and c .

Solve the separable differential equation d y d x = 0 . 3 y , and find the particular solution satisfying the initial condition y ( 0 ) = - 2 . y ( x ) =

Use the limit laws to find the limit . 2 2 3 3 lim 1 2 x x x x x +

Find the derivative of the function y = 7 x 1 - 4 x 2 e - 2 x ( s i n 2 ( x ) ) using logarithmic differentiation. Be sure to include parentheses around the arguments of any trigonometric functions in your answer.

when is the t value small when eta squared is large?

Find the derivative of f ( x ) = l n ( 3 x 8 4 x 4 2 ) , wing the properties of the loganthm .

LARCALC 1 2 2 . R . 0 4 3 . Use the Product Rule or the Quotient Rule to find the derivative of the function. y = 2 x 5 s e c ( x )

Write down the derivatives of the following standard functions in the boxes provided. The derivative of f ( x ) = c where c is a real number is given by f ' ( x ) = The derivative of f ( x ) = e x is given by f ' ( x ) = The derivative of f ( x ) = x n where n is a real number is given by f ' ( x ) =

2 1 : 5 9 5 Gw ( 3 ) 1 pt 1 1 8 ( i ) Details Assume that the integral 0 3 2 x 6 f ( x , y ) d y d x exists. Which is the equivalent double integral with the order of integration changed? 0 6 y 2 3 f ( x , y ) d x d y 0 3 6 2 y f ( x , y ) d x d y 2 x 6 0 3 f ( x , y ) d x d y 0 6 0 y 2 f ( x , y ) d x d y 0 3 2 x 6 f ( x , y ) d x d y Question

lim n t a n - 1 n = Select one: a . b . 0 c . 3 2 d . 2

derivate this: f ( x ) = ( 4 - x 2 ) 3

Suppose lim x 7 f ( x ) = 0 and lim x 7 g ( x ) = - 6 . Find lim x 7 ( 8 - f ( x ) - 5 g ( x ) ) .

Evaluate the following. Give answers exactly. cos ( arcsin ( 0 ) ) = tan ( arcsin ( 2 / 2 ) )

Calculate lim x l n ( 3 x ) x 3 Solution Since l n ( 3 x ) and , a s x , l'Hospital's Rule applies. lim x l n ( 3 x ) x 3 = lim x 1 x 1 3 x - 2 3 = lim x 1 x 1 ( x 2 3 ) unnecessary. lim x l n ( 3 x ) x 3 = lim x 1 x 1 ( x 2 3 ) = lim x 3 x 3 =

Find lim x 0 ( x 4 2 - 2 x )

calculate the instantaneous rate o f change a t x = 1 o f the function f ( x ) = x 2 l n ( 2 x 2 - 1 )

Let r ( t ) = 4 7 t + 1 , 5 t 7 t 2 + 6 , 5 t 2 6 t 3 4 r ( t ) = - 4 - 7 t + 1 , 5 t 7 t 2 + 6 , - 5 t 2 - 6 t 3 - 4 Find r ' ( t ) r ( t ) r ' ( t ) = r ( t ) = , , , ,

Find the limit . ( If an answer does not exist, enter DNE. ) lim x 3 x 2 + 2 x 1 5 x 2 9

Find the average rate of change of the function fix ) = 1 x - 6 as x charges from x = - 1 fo x = 0

Find the directional derivative o f f a t the given point i n the direction indicated b y the angle . f ( x , y ) = 8 x + 9 y , ( 9 , 1 ) , = - 6 Duf ( 9 , 1 )

Find the l i m i t . lim ( x , y ) ( 2 , 4 ) e x y

Evaluate the integral. 1 e l n 5 x d x = , ( T y p e a n exact answer. )

Example 1 : a n = 3 n 1 n 4 Find the limit of the sequence as n .

Evaluate the integral 1 6 9 + 2 5 r 2 d r 1 6 9 + 2 5 r 2 d r =

Use the Chain Rule to find d w d t . w = x e y z , x = t 3 , y = 1 - t , z = 4 9 t

Find the sum o f n = 1 n ( n + 1 ) x n = for

Differentiate. y = ( z 5 + e z ) z 2 y ' = e z z ( 1 2 ) + ( 1 1 z ( 9 2 ) 2 ) + ( e z 2 z ( 1 2 ) )

Find the acute angle between the intersecting lines x = 2 t , y = 6 t , z = - 3 t and x = 1 - 3 t , y = 1 4 2 t , z = 6 t . The angle is radians. ( Round to the nearest thousandth as needed. )

Find the distance from the point ( - 6 , 3 , 5 ) to the a . x y - plane b . y z - plane c . x - plane. a . The distance from the point to the x y - plane is ( Type an exact answer, using radicals as needed. )

This question: I powing State the domain and renge of the function. f ( x ) = 1 0 0 - x 2 2 The downin is The renge is ( Simpliy your answer. Type your anwwer in intervel rotation. )

Use the substitution formula to evaluate th 0 1 x 1 2 d x 4 3 2 2 3 2 2 - 3 2 2 2 - 1 4 3 2 2 - 2 3 Question 6 ( Mandatory ) ( 1 point ) Listen Find the area of the shaded region. y = x 2 - 4 x 3

Find the point on the line y = 5 x + 4 that is closest to the origin. ( x , y ) = 4 5 , 2 1 3

Evaluate the indefinite integral. 3 x - 3 ( 3 x 2 - 6 x 5 ) 3 d x C

Evaluate the definite integral. 0 3 s i n 2 ( x ) c o s 3 ( x ) d x ( E x p r e s s numbers i n exact form. Use symbolic notation and fractions where needed. ) 0 3 s i n 2 ( x ) c o s 3 ( x ) d x =

Differentiate. g ( x ) = 2 x - 1 6 x 5 x 3 g ' ( x ) =

Calculate the fluid force on one side of a semicircular plate of radius 6 th that rests vertically on its diameter at the bottom of a pool filled with water to a depth of 7 fi . Assume the weight - density of water is 6 2 . 4 l b f t 3 . The fluid force on one side of the plate is ( Round the final answer to the nearest tenth as needed. Round all

1 2 points possible Answered: 3 / 1 2 0 2 prop,vdots 1 p t 1 Details Evaluate the following expression. Round value to 2 decimal places if needed. 3 5 0 0 * ( 1 . 0 4 2 ) - 1 9 =

Let f ( x ) = s i n x * c o s x , then f ' ( x ) = ? ( a ) f ' ( x ) = c o s x * ( - s i n x ) ( b ) f ' ( x ) = c o s x * s i n x ( c ) f ' ( x ) = c o s 2 x + s i n 2 x ( d ) f ' ( x ) = c o s 2 x - s i n 2 x

Suppose functions f and g are continuous at a in R . Let c be a real number. If g ( a ) 6 = 0 then f g is continuous at a

A baseball is hit from a height of 3 . 6 feet above the ground with an initial velocity of 1 7 7 feet per second and at an angle of \ ( 3 2 ^ { \ circ } \ ) above the horizontal. What is the maximum height reached by the baseball? Neglect air resistance. The fence at the edge of the field is 8 feet tall and located 3 8 5 feet from home plate. Will

The Trapezoidal Rule with n = 2 0 is used to approximate x ^ - 2 f ind a the smallest possible upper bound for the error in this approximation to 4 decimal places. 0 . 0 0 1 0 0 . 7 4 8 2 0 . 7 5 3 7 0 . 0 3 3 8 0 . 7 5 0 0 0 . 0 1 6 9 4 1 x 2 dx . Using the error bound formula

Evaluate the following improper integral o r conclude that i t diverges: 1 2 l n x x 2 d x Select one: a . 3 b . diverges c . 2 d . 1 2

QUESTION 7 Find f ' ( x ) . , f ( x ) = x 4 t a n 2 x

Differentiate the function. y = ( 1 6 - x ) 5 0 d y d x =

3 attempts left Compute the volume of the solid bounded by the surfaces z = 1 - y 2 , z = 0 , x = 2 5 , and x = 2 8 . r e g i o n d z d y d x =

Compute the exact work done by the force field F ( x , y , z ) = ( : 5 y , 5 x , 6 y : ) acting on an object as it moves along the helix defined parametrically by x = 3 c o s ( f ) , y = 3 sin ( f ) and z = 2 f , frem the point ( 3 , 4 , 4 ) to the point ( - 3 , 0 , 2 ) . W =

f ( x ) = 0 x 2 The curvalure function is ans )

1 . 2 I f g ( p ) = p p + 1 and h ( p ) = p + 1 p + 2 . Find the domains o f the functions: a . , g * h

simplify ( x ^ 4 ) * ( x ^ - 4 ) / ( x ^ - 8 )

The line yequals = 2 xplus + 7 7 is a slant asymptote of the function f left parenthesis x right parenthesis equals StartFraction 2 x squared plus 7 x Over x minus 3 EndFractionf ( x ) = 2 x 2 + 7 xx 3 . Choose the best answer below.

USE a Basic Rule, u - sub ( s h o w u & d u , use change o f boundaries, when appropriate ) o r IBP ( s h o w u , d v , d u and v - a s always ) t o INTEGRATE: , l n ( 4 + x 2 ) d x

Find the derivative of the function. y = sq rt 5 + 2 e 3 x

Find the slope ( 7 , - 2 ) and ( 7 , - 4 )

Use integration by parts to find 5 x 2 cos ( 3 x ) dx .

[ - / 4 Points ] Take the derivative of ( x y ) 3 = 3 x - 4 y 5 with respect to the variable t . Do not rearrange and move terms to the other slide of the equation. Answer:

Given lim x 2 f ( x ) = 3 and lim x 2 g ( x ) = - 3 , evaluate: lim x 2 ( - 8 f ( x ) 3 g ( x ) ) =

Use the chain rule t o find the derivative o f 2 ( 5 x 1 0 + 7 x 9 ) 1 9 You d o not need t o expand out your answer.

E For the following parametric equation, eliminate the parameter t and rewrite i t a s a cartesian equation. x ( t ) = e - 2 t and y ( t ) = 2 e - t y = 2 x 2 y = e 2 x y = e l n ( x ) y = 2 x 2

Evaluate the limit lim s 5 1 s + 3 - 1 8 s - 5

Find d s ( d ) t , s = 3 t 2 - s i n t 2 e t

Write the equations of the vertical and horizontal asymptotes for the function: x + 2 y = X - 5 Be sure to use " x = " and " y = "when you write the asymptotes.

Suppose you start at the origin, move along the x - axis a distance of 9 units in the positive direction, and then move downward a distance of 5 units. What are the coordinates of your position?

Evaluate the integral using integration by parts with the indicated choices of u and d v . ( Use C for to 2 c o s ( ) d ; , u = 2 , d v = c o s ( ) d

Let F ( x ) = f ( x 9 ) and G ( x ) = ( f ( x ) ) 9 . You also know that a 8 = 1 5 , f ( a ) = 3 , f ' ( a ) = 1 4 , f ' ( a 9 ) = 4 Then F ' ' ( a ) = and G ' ( a ) =

Find the intervals en which f ( x ) is increaning, De intervals on which fix ) is decreasing, and the relative exerme points. 1 ( x ) = 3 x 4 - 8 4 x 3 1 7 Find the intervals on which f ( x ) is increasing. Select the correct choice below and, f necessafy, fill in the antere box to complete your choioe. A . The function is increasing on ( Type

Current Attempt in Progress Use the Fundamental Theorem to evaluate the definite integral exactly. 0 4 ( 9 x 2 5 ) d x Enter the exact answer. 0 4 ( 9 x 2 5 ) d x =

For the following function, make a table of slopes of secart lines and make a corjecture about the slope of the tangent line at the indicated point. f ( x ) = 6 c o s x a t x = x 2 Complete the table below. decimal places as needed ) \ table [ [ interval , Siope of secant line ] , [ 2 , , - 3 2 0

Problem \ # 7 : Find the surface area of the part of the plane \ ( 5 x + 3 y + 6 z = 1 5 \ ) that lies in the first octant. Problem \ # 7 : sqrt ( 4 3 7 5 ) / 2 Enter your answer symbolically, as in these examples Submit Problem \ # 7 for Grading
$Problem \ # 7 : Find the surface area of the part$

( 3 ) lim t - 3 t + 2 4 t 2 + 3 t 2 + 5 .

[ - / 1 Points ] SCALCET 9 M 7 . 2 . 0 0 1 . MI . Evaluate the integral. ( Use C for the constant of integration. ) 1 5 s i n 3 ( x ) c o s 2 ( x ) d x SCALCET 9 M 7 . 2 . 0 0 2 .

1 s i n x + c o s x derivitive

Evalyate the following integral using integration by parts. 0 3 x c o s x d x Use the integration by parts formula so that the new integral is simpler A . ( - 3 c o s x ) | 0 - 0 ( s i n x ) d x | B . ( 3 x ) | 0 - 0 ( - 3 c o s x ) d x | C . ( 3 x s i n x ) | 0 - 0 ( 3 s i n x ) d x | D . ( 3 c o s x ) | 0 - 0 ( 3 x ) d x | . Evaluate the

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