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subject categories
sciences
mathematics
june 2018
5

Mathematics Questions and Answers June 5, 2018

Expert-verified solutions to help you succeed

Find a set o f parametric equations o f the line that passes through the points ( 5 , 2 , 3 ) and ( - 2 , 6 , 0 ) . ( 1 0 points )

Question 1 4 ( 1 point ) Evaluate l o g 3 ( 1 0 2 4 2 4 3 ) - 2 9 / 1 6 - 1 0 1 0 5 Question 1 5 ( 1 point ) The ratio of inlenaities of twe sewhy is 6 4 7 . 1 7 fice holer sampl has a decibel level of 9 7 abs , what is the decel of the ofthat ugind?

Find the area under the curve y = 5 x 3 from x = 1 tot = 1 0 Fantastic job!t = 1 0 0 Great work!t = 1 , 0 0 0 Excellent job! Find the total area under this curve for x 1 .

QUSTIDN S = 1 PONT Find the derivathe of y = 9 x - 1 . Be sure to include paremenes arsund the arguments of anylogardmic fonctions in your answer. Provide your answer below: y ' =

Compute the following limits - if possible. State the method ( s ) you are using, and use proper notation. ( a ) lim x 0 ( e x - e - x - 2 x x 2 )

Determine whether the series is convergent or divergent. If it is cony 1 4 3 1 6 1 6 4 3 2 5 6 1 1 0 2 4 3 4 0 9 6 cdots Need Hels? Need Help?

For the following series, use the Comparisos. Tast or the Limit Comparious Test ( and ONLY these too testa ) to find the best answer the following questions. ( a ) n = 1 2 n ( n 1 ) ( b ) n = 1 1 2 n - 1 ( c ) n = 1 1 n s i n 2 ( 1 n ) ( d ) n = 1 s i n ( 1 n ) n 2 Converge Diverges No Information Gained Converges Diverges No Information Gniand

Problem 8 8 . Revenue and profit functions. A company manufactures 1 0 - and 3 - speed bicycles. The weekly demand and cost functions are p = 2 3 0 - 9 x y q = 1 3 0 x - 4 y C ( x , y ) = 2 0 0 8 0 x 3 0 y where $ p is the price of a 1 0 - speed bicycle, $ q is the price of a 3 - speed bicycle, x is the weekly demand for 1 0 - speed bicycles, y is

For what values of t between 0 and 2 is the parametric curve generated by the equations x = c o s 3 t , y = s i n 3 t concave up ? ( 0 , 2 ) ( 0 , ) ( 0 , 2 ) ( 2 , ) ( 0 , 4 ) ( 0 , 2 )

Calculate the value of the following iterated integral. \ int _ 0 ^ 4 \ int _ ( \ sqrt ( y ) ) ^ 2 \ sqrt ( x ^ ( 3 ) + 1 ) dxdy

Evaluate the definite integral. 2 ( 2 x 9 ) ( 4 x 2 + 5 ) dx 0

Determine whether the sequence converges or diverges. If a n = e - 4 n 2 lim n a n = Need Help?

For the function f ( x ) = 3 e - x 3 , find f ' ' ( x ) . Then find f ' ' ( 0 ) and f ' ' ( 2 ) . f ' ' ( x ) = 9 x e - x 3 ( 3 x 3 - 2 ) Select the correct choice below and fill i n any answer boxes i n your choice. A . f ' ' ( 0 ) = 0 ( S i m p l i f y your answer. ) B . f ' ' ( 0 ) i s undefined. Select the correct choice below and fill i n any

Evaluate the integral. ( R e m e m b e r the constant o f integration. ) 4 5 + 4 x - x 2 2 d x

Find the volume of the solid situated in the first octant and bounded by the planes x 2 y = 1 , x = 0 , y = 0 , z = 4 , and z = 0 .

code class = "asciimath" > ( cosx ) / ( senxcotx ) = 1

indicate a good method for evaluating the integral \ int \ frac { x + 4 } { x ^ 2 + 8 x + 6 } dx

Use the Ratio Test to determine the interval of convergence of \ sum _ ( n = 1 ) ^ ( \ infty ) ( x ^ ( n ) ) / ( \ root ( 1 2 ) ( n ) * 4 ^ ( n ) ) * , * \ infty for infinity, u for combining intervals, and an appropriate type of parenthesis " ( " , " ) " , " [ " or " ] " depending on whether the interval is open or closed. Enter DNE if interval

( Jatory ) Differentiate the function. y = 4 x 2 - 1 6 x 3 5 y ' =

Evaluate the integral involving hyperbolic functions. c o s h ( x ) 4 s i n h ( x ) + 1 1 d x C for the arbitrary constant. Absorb into C a s much a s possible. c o s h ( x ) 4 s i n h ( x ) + 1 1 d x =

Find the derivative of the following function h ( x ) = 7 x 2 2 x 2 7 h ' ( x ) =

Calculate the Taylor polynomials T 2 and T 3 centered a t a = 2 for the function f ( x ) = x 4 - 2 x . ( U s e symbolic notation and fractions where needed. ) T 2 ( x ) T 3 ( x ) =

C for the constant of integration. \ int ( x ^ ( 2 ) ) / ( \ sqrt ( 9 - x ^ ( 2 ) ) ) dx
$C for the constant of integration. \ int ( x ^ ($

Find the most general antiderivative of the function h ( x ) = ( 3 x 4 - 6 x 5 1 2 ) . Use an upper - case C for any arbitrary constants. H ( x ) =

[ 1 0 ] Evaluate the integral E z - x 2 - y 2 d V where E is the region bounded by the cylinder given by x 2 y 2 = 9 , x 0 , y 0 , 0 z 5 .

Find the centex, food, and vertices of the hyperbola. 1 6 y 2 - x 2 2 x 6 4 y 1 5 = 0 center ( x , y ) = ( 1 , - 2 , ) focus ( smaller y - value ) , ( x , y ) = ( 1 , 2 5 1 2 ) focus ( larger y - value ) , ( x , y ) = ( 1 , - 2 5 1 2 ) vertex ( amaller y - value ) , ( x , y ) = ( 1 , 2 3 2 , x ) wertex ( arger y - value ) , ( x , y ) = ( 1 , - 2 3

lim to infinity of ( ( 3 / 5 ) ^ n ) / ( ( n ^ 2 ) / ( 5 ^ n ) 1 )

Find the work done b y the force field F ( x , y , z ) = 1 + 1 y j + 4 k o n a particle that moves along the helix r ( t ) = 2 c o s ( t ) i + 2 s i n ( t ) j + 6 t k , 0 t 2

Question 5 ( M a n d a t o r y ) ( 1 point ) Express the solution t o 2 3 3 + 6 x 8 x - 7 5 4 7 5 + 6 x i n set notation. a ( 3 5 . 8 0 , 5 9 . 3 8 ) b { x h a t ( I ) R | 3 5 . 8 0 x 5 9 . 3 8 } c { x h a t ( I ) R | 1 5 4 x 2 7 5 } d ( 1 5 4 , 2 7 5 )

Problem 1 Find the value of the third non - zero term in the binomial series expansion of f ( x ) = 1 x 2 . ( a ) - 1 2 x 2 ( b ) ) - 1 8 x 2 ( c ) 1 8 x 2 ( d ) 1 2 x 2 ( e ) 3 8 x 2 Problem 2 1 1 2 x 1 2 1 2 ( - 1 2 ) = ( 1 x ) 1 2 1 2 ( 1 2 - 1 ) 2 ! - 1 4 * 1 2 =

f ( x ) = 2 4 x 3 2 - 8 x 1 2

Question Determine the domain that results from eliminating the parameter in the set of parametric equations below. x ( ) = - 5 s i n ( ) y ( ) = 4 c o s ( ) Enter your answer using interval notation. Provide your answer below:

Use any method to evaluate the integral. 0 5 2 2 2 5 x 2 d x ( 2 5 - x 2 ) 3 2

If f ( x ) = x 3 + 8 x , estimate f ' ( 3 ) using the table below. \ table [ [ x , 2 . 9 9 8 , 2 . 9 9 9 , 3 , 3 . 0 0 1 , 3 . 0 0 2 ] , [ x 3 + 8 x , 5 0 . 9 3 0 , 5 0 . 9 6 5 , 5 1 , 5 1 . 0 3 5 , 5 1 . 0 7 0 ] ] Round your estimate to the nearest integer.

QUESTION 1 5 * 1 POINT Find a power series for f ( x ) = 4 9 x + 1 5 x 2 + 4 x - 1 centered a t 0 b y adding two power series. Provide your answer below: n = 0 ( , ) x n

Find the k F F = ( x e 8 y ) i + ( y e 9 x ) j ( c u r l F ) * k =

Let lim x 4 f ( x ) = 7 and lim x 4 g ( x ) = 5 . Use the limit rules to find the following limit . lim x 4 f ( x ) g ( x ) 6 g ( x ) lim x 4 f ( x ) g ( x ) 6 g ( x ) = ( Simplify your answer. Type an integer or a fraction. )

Tatardar Frevelthe Find the Initi, Use Riospitals Rule If appropriabe. If there is a more elementary method, consider using if . lim x l n ( 5 x ) 5 x 2 Stup 1 As x - , l n ( 5 x ) - and 5 x 2 stepe Therefore lim x l n ( 5 x ) ? 2 5 x is indeberminate of trpe * * * * . We must use Riospital's Rule. The derivative of in ( 5 x ) is and the

Draw a sketch o f the function that has the following properties: f ( - 2 ) , f ( 1 ) , and f ( 5 ) = 0 . f ( x ) 0 when - 2 5 f ( x ) > 0 when x - 2 and 1 4 f ' ( x ) > 0 when - 1 2 f ' ' ( x ) > 0 when x 2 Your graph must have a n accurately labeled horizontal scale

A manufacturer cuts squares from the corners of a rectangular piece of sheet metal that measures 3 inches by 8 inches. The manufacturer then folds the metal upward to make an open topped box. Letting x represent side lengths in inches of the squares find the value of x that maximizes the volume enclosed by the box. Then give the maximum volume

Calculate the derivative for f ( x ) = ( x + 3 ) ( x - 1 ) ( x - 8 ) . ( U s e symbolic notation and fractions where needed. ) f ' ( x ) =

Find the Derivatives y = e ^ x ^ 4 ln 4 x ^ 2

Suppose z = x ^ 2 siny , x = 3 s ^ 2 - 2 t ^ 2 , y = - 4 st . A . Use the chain rule to find and as functions of x , y , s and t .

Jmework 4 Question 9 , 1 2 . 2 . 3 Differentiate. f ( x ) = e x 5 2 x f ' ( x ) =

For f ( x , y ) , x = r c o s and y = r s i n find d e l 2 f d e l 2 d e l 2 f d e l r 2 .

Find the indicated integrals: x 2 6 x 4 2 d x = ( 1 ) C

[ 1 5 ] Evaluate the surface integral S F * d S , where F = - - y j k and S is given by the equation r ( u , v ) = ( : u 2 - 2 v , u v , u v 2 : ) , 0 u 1 , 1 v 4 .

Find the arc length of the graph of the function over the indicated interval. ( Round your answer to five declmal phaces. ) y = l n ( e x 1 e x - 1 ) , [ l n ( 4 ) , l n ( 5 ) ]

Express the following sums using sigma notation. a . 7 8 9 1 0 1 1 b . 9 1 8 2 7 3 6 4 5 5 4 c . 1 5 2 5 3 5 4 5 d . 1 1 2 1 3 1 4 a . 7 8 9 1 0 1 1 = k = 1 5

Question 4 Find the derivative of the function g ( x ) = e x 4 - 4 x g ' ( x ) =

- 8 8 . 3 6 = ( ( 1 ) / ( x ) ) ^ ( - 1 ) what is x ?

Evaluate the definite integral. 2 ( 6 x 3 ) ( 4 x 2 + 6 ) dx 0

Find the Laplace transform of f ( t ) = { 0 t ^ 2 for t < 3 t > = 3 Rewrite the function f ( t )

Consider the parametric equations below. x = t 2 4 , y = t + 2 , 3 t 3 liminate the parameter to find a Cartesian equation of the curve. for 1 y 5

Provide an appropriate response. Find f ' ' ( x ) for f ( x ) = - 7 x 9 5 x 2 . f ' ' ( x ) = 5 0 4 x 8 1 0 f ' ' ( x ) = - 5 0 4 x 7 1 0 f ' ' ( x ) = 5 0 4 x 7 - 1 0 f ' ' ( x ) = - 6 3 x 8 1 0 x

t = 1 0 l n ( 2 ) 2 4 0 3 2 0 1 T - 1 0 0 d T

Evaluate the definite integral 0 1 3 x ( 1 + 2 x 2 ) 2 3 d x

Solve x l n x d x using integration by parts. x 2 2 l n x - x 4 8 C x 2 2 l n x x 2 4 C x 2 2 l n x - x 2 4 C x 2 2 l n x x 4 8 C

The average number o f customers, c , a t a 2 4 hour sandwich shop per hour i s modelled roughly b y the equation c ( h ) = - 5 c o s ( h 1 2 ) + 1 2 , with h = 0 representing midnight. How many hours per day are there a t least 1 3 customers per hour, t o the nearest hour? What time o f day i s peak business?

Evaluate each of the following integrals, using a trigonometric substitution. Do not forget the back substitution. Solutions using other methods are not acceptable. ( a ) dx 4 x 2 + 1 \ int \ frac { dx } { \ sqrt { 4 x ^ 2 + 1 } } 4 x 2 + 1 dx ( b ) 1 x 2 1 6 x 2 dx \ int \ frac { 1 } { x ^ 2 \ sqrt { 1 6 - x ^ 2 } } dx x 2 1 6 x 2 1 dx ( c ) x 2

Evaluate the integral using one of the formula choices given below. 4 x 4 x 4 4 9 dx du u 2 a 2 = ln u + u 2 a 2 + C duu 2 u 2 a 2 = u 2 a 2 a 2 u + C du a 2 + u 2 = ln ( u + a 2 + u 2 ) + C a 2 u 2 u 2 du = a 2 u 2 u sin 1 ( u 2 ) + C Be sure to include the arguments of any logarithmic or trigonometric functions in parentheses.

Evaluate the triple integral E x y z d V where E i s the solid: 0 z 3 , 0 y z , 0 x y .

Find the interval o f convergence. n = 4 x n n 9 for infinity, U for combining intervals, and a n appropriate type o f parenthesis " ( " , " ) " , " [ " , " ] " depending o n whether the interval i s open o r closed. Enter O ? i f the interval i s empty. Express numbers i n exact form. Use symbolic notation and fractions where needed.xinI

Evaluate the integral. 0 1 / 3 t ^ 8 + 1 / 4 t ^ 7 t dt 2

Test the series for convergence o r divergence using the Alternating Series Test. n = 0 s i n ( ( n + 1 2 ) ) 3 + n 2 Identify b n . Evaluate the following l i m i t . lim n b n Since lim n b n , 0 and b n + 1 , b n for all n ,

what i s d x x 2 - 2 x + 8 2 ?

Using the guidelines for integrating b y parts, carefully choose which expression i s u , d u , d v and v . D o not evaluate the integral. x 6 l n ( 3 x ) d x , u = , d v = d u = , v =

SCalcET 9 1 1 . 5 . 0 1 1 . Test the series for convergence or divergence using the Alternating Series Test. \ infty ( 1 ) n n 2 n 3 9 n = 1 Identify bn . Evaluate the following limit . lim n - > \ infty bn Since lim n - > \ infty bn 0 and bn 1 bn for all n > 3 , .

Find the flux o f the constant vector field vec ( v ) = vec ( i ) - vec ( j ) + 4 vec ( k ) through a square plate o f area 9 i n the y z - plane oriented i n the positive x - direction. Enter a n exact answer. Flux =

Use the chain rule to calculate f ( x ) , if f ( x ) = d d x - x 4 x 4 e t 1 0 d t . f ( x ) =

lim x 0 ( 8 x - 8 | x | )

Write the first four terms of the sequence { a n } n = 1 . a n = 6 n 1 2 n 7

A n electronic games manufacturer producing a new product estimates the annual sales t o b e 5 0 0 0 units. Each year 2 % o f the units that have been sold will become inoperative. S o , 5 0 0 0 units will b e i n use after 1 year, 5 0 0 0 + 0 . 9 8 ( 5 0 0 0 ) units will b e i n use after 2 years, and s o o n . How many units will b e i n use

( 1 point ) Let f ( x ) = - x 4 - 7 x 3 2 x 6 . Find the open intervals on which f is concave up ( down ) . Then determine the x - coordinates of at inflection points of f . f is concave up on the interval f is concave down on the intervals The inflection points occur at x : Notes: In the first two, your answer should either be a single interval,

Find the area between z = o , 1 . 7 2

Evaluate the limit lim y 0 1 ( 8 y ) 2 - 1 6 4 y

( Question 1 ) 2 0 points Find the indicated derivatives if A is a real number constant. a . d d t ( l n ( t 2 ) 4 t 2 ) b . For y = Asec ( A x ) c o s ( s i n ( A x ) ) , find y . c . For f ( x ) = 1 e x e x , find f ' ( x ) d . Find d 3 d 3 ( s i n ( A ) ) Assessment Details Calculator 1 2 rut.

Question 6 ( M a n d a t o r y ) ( 1 point ) Estimate the instantaneous rate o f change o f the function f ( x ) = 1 6 x 2 - 2 5 a t x = - 7 . Round your answer t o the nearest whole number. a

e integral. ( Hint: Use u - substitution ( b ) ( 2 x 1 ) e x 2 x d x

Find a formula for the general term a n of the sequence assuming the pattern of the first few terms continues. { 5 , 5 3 , 5 9 , 5 2 7 , 5 8 1 , cdots } Assume the first term is a 1 a n =

Let L be the language consisting of strings of 0 ' s and 1 ' s with an even number of 1 ' s Which of the following is a regular expression that defines ? ? ? ? 1 0 * * ( 0 * * 1 0 * * 1 0 * * ) * * 0 * * 1 0 * * ( 0 * * 0 1 * * 0 1 * * ) * * 1 * * 0 * * ( 0 * * 1 0 * * 0 1 * * ) * * 1 0 * * ( 0 * * 1 0 * * 1 0 * * ) * * 0 * * 0 * * ( 1 * * 1 0 * *

Write the sum ( 7 5 + 7 ) + ( 7 6 + 7 ) + ( 7 7 + 7 ) + ( 7 8 + 7 ) i n summation notation i n terms o f k . ( U s e symbolic notation and fractions where needed. ) k = - 8

Find the derivative of the function. y = 7 x 2 - x ( 5 x - 4 ) 9 d y d x =

investment i n constant 2 0 2 0 dollars i s V ( I , R ) = 4 , 0 0 0 [ 1 + 0 . 0 5 ( 1 - R ) 1 + I ] 1 0 Use this function o f two variables t o complete the table. ( R o u n d your answers t o two decimal places. )

Question 4 ( 1 point ) Which of the following is an even function? y = 5 x 2 ( x - 2 ) y = - 3 x ( x - 2 ) y = 2 x 3 ( x 3 - x ) y = x 2 ( x 2 x )

The time it takes for one complete swing of a pendulum is called the period of its motion. The period T ( in seconds ) of a swinging pendulum is found using the formula T = 2 L 3 2 2 where L is the length of the pendulum in feet and 3 2 is the acceleration of gravity in feet per square second. Round your answers to one decimal place. a . Find the

Find the indefinite integral. ( Remember the constant of integration. ) tan 3 4 ( 5 x ) sec 2 ( 5 x ) dx

Find the critical points of the following function. Use the Second Derivative test to determine ( if possible ) whether each critical point corresponds to a maximum, minimum, or saddle point. f ( x , y ) = x 2 x - 3 x y y 3 - 5

Evaluate the integral using Integration b y Parts. 4 s i n - 1 ( x ) d x C for the arbitrary constant. Absorb into C a s much a s possible. 4 s i n - 1 ( x ) d x =

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