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subject categories
sciences
mathematics
june 2018
14

Mathematics Questions and Answers June 14, 2018

Expert-verified solutions to help you succeed

Evaluate the following limit . lim ( x , y , z ) ( 1 , l n 4 , 5 ) z e x y

Find the derivative of the function. f ( x ) = - 1 2 x 5 2 3 x 1 . 5 x f ' ( x ) =

[ - / 1 Points ] Given that lim x 2 f ( x ) = 1 , lim x 2 g ( x ) = - 2 , lim x 2 h ( x ) = 0 find each limit , if it exists. ( If an answer does not exist, enter DNE. ) ( a ) lim x 2 [ f ( x ) + 4 g ( x ) ] ( b ) lim x 2 [ g ( x ) ] 3 ( c ) lim x 2 f ( x ) 2 ( d ) lim x 2 2 f ( x ) g ( x ) ( e ) lim x 2 g ( x ) h ( x ) ( f ) lim x 2 g ( x ) h ( x

Find the general solution of the given differential equation. ( x 2 9 ) dydx + 6 y = ( x + 3 ) 2 Give the largest interval over which the general solution is defined. ( Think about the implications of any singular points. Enter your answer using interval notation. )

T H - 2 2 4 3 - 0 2 F ( 5 , 6 , - 8 ) parallel t o the z - axis. Choose the correct answer below. A . x = 5 + t , y = 6 + t , z = - 8 , - x = - 5 + t , y = - 6 + t , z = 8 , - D . x = 5 + t , y = 6 + t , z = - 8 , - x = - 5 , y = - 6 , z = 8 + t , - C . x = - 5 + t , y = - 6 + t , z = 8 , - D . x = 5 + t , y = 6 + t , z = - 8 , - x = 5 , y = 6 , z

Find the volume of the region bounded by h ( x ) = ln ( x + 2 ) , y = 0 , x = 2 when revolved around x = - 2

Show me the steps to solve second derivative respect to y of ( ( e ^ x ^ 3 ) + y ^ 3 ) / ( x ^ 2 )

0 - 6 years each given a percentage of time employees will stay with a company. how to find the average amount of time

Determine the following limit . lim x 4 2 x 3 5 x 2 - 5 x 4 9 x 3 x 2 5 x 1 Select the correct cholce below and, if necessary, fill in the answer box to complete your choice. A . lim x 4 2 x 3 5 x 2 - 5 x 4 0 x 3 x 2 5 x 1 = ( Simplify your answer. ) B . The limit as x approaches does not exist and is neither nor - .

Solve the given differential equation. x 2 y ' ' 9 x y ' 7 y = 0 y ( x ) =

[ - / 1 Points ] SCalcET 9 1 0 . 4 . Find the area of the region that lies inside the first curve and outside the second curve. r = 8 s i n ( ) , r = 4 Need Help? 4 . [ - / 1 Points ] SCalcET 9 1 0 .

Find f ( x ) if f ' ( x ) = 3 / 1 x 2 and f 1 2 = 9 . f ( x ) =

Solve the differential equation given below. d y d x = - 4 y ( - 3 - y )

Your best submission for each e [ - / 1 Points ] 0 / 3 Submissions Find the indefinite integral. ( Remen s i n ( x ) d x Need Help?

The number of employees for a certain company has been decreasing each year by 2 % . If the company currently has 7 8 0 employees and this rate continues, find the number of employees in 1 1 years.

Determine d 2 d x 2 [ e 3 x ] Select one: a . 3 e 9 x b . 9 e 3 x c . 3 e 3 x d . 9 x 2 e 3 x

Find the intervals on which f ( x ) = x 3 - 7 5 x + 8 decreases.

7 1 - 7 2 Find the distance freen the point to the given plane. 7 1 . ( 1 , - 2 , 4 ) , 3 x 2 y 6 z - 5

Use the l i m i t definition o f the derivative t o find the instantaneous rate o f change o f f ( x ) = 5 x 2 + 7 x + 6 a t x = 1

Verify that y = - 3 t c o s ( t ) - 3 t is a solution of the following initial - value problem. so y is a solution of the differential equation. Also y ( ) = , so the initial condition is satisfied.

Let F ( x ) = x 2 x 2 2 . Make sure to show complete and correct work to carn full credit. ( a ) Determine the domain of F ( x ) . ( b ) Evaluate F ( 4 ) ( c ) Find a number b such that F ( b ) = 3 . ( d ) Determine the average rate of change of F ( x ) from x 1 = 2 to x 2 = 7 .

lim x 0 ( x 1 ) l n a x with a > 0 , a 1 , is an indeterminate form of type 0 0 , 0 , 1 ( circle one ) . Show that lim x 0 ( x 1 ) l n a x = a .

Evaluate the definite integrals using properties of the definite integral and the fact that - 3 4 f ( x ) d x = - 6 , 4 7 f ( x ) d x = 1 0 , and 4 7 g ( x ) d x = 2

A rational function f ( x ) is defined for all real numbers except for x = - 6 and x = 4 . We are given that x = - 6 and x = 4 are vertical asymptotes for f ( x ) . The first derivative of this function is given below: f ' ( x ) = x 2 - 1 ( x + 6 ) 3 ( x - 4 ) 3 List all local extreme points for f ( x ) .

Solve the following triangle. A = 4 4 , C = 5 7 , a = 7 5 c m B = 7 9 ( Simplify your answer. ) b ~~ cm ( Round to the nearest tenth as needed. )

Using the equation Y = 2 3 1 . 5 ( x ) with coefficient R 2 . 3 6 5 , what could you conclude about the relationship between X and Y ?

Determine lim x 0 + l o g 7 x + x 2 l o g 1 4 x - 2 x 4

Let f ( x ) = { 7 x - 1 i f x 7 - 2 x b i f x > 7 If f ( x ) is a function which is continuous everywhere, then we must have b = Now for fun, try to graph f ( x ) .

Evaluate the integral. 0 4 ( 4 - t ) t 2 d t

Differentiate the function. h ( x ) = 3 4 ( x 5 3 x 3 + 6 ) 8

QUESTION 1 0 * 1 POINT Determine whether the Comparison Test will prove whether the integral 4 2 2 x 3 + 4 d x converges o r diverges b y comparing i t t o the integral 4 1 x 3 d x , o r i f i t will b e inconclusive. Select the correct answer below: Converges Diverges Inconclusive

Beam JW . Orthopedic Taping, Wrapping, Bracing & Padding. 4 th ed . Philadelphia, PA: F . A . Davis Company; 2 0 2 1

An approach path for an aircraft landing is shown in Figure 3 . 2 5 and satisfies the following conditions: ( i ) The cruising altitude is h when descent starts at a horizontal distance l from touchdown at the origin. ( ii ) The pilot must maintain a constant horizontal speed v throughout descent. ( iii ) The absolute value of the vertical

Suppose there is a large funnel that is 1 2 meters deep and 9 meters in radius at the top. The tank is filled to the top. A pump is placed at the top of the tank. Find the work done to empty tank to depth of 1 meter

( 2 0 p t s ) A particle moves along the triangle with vertices ( 1 , 0 , 0 ) , ( 0 , 1 , 0 ) and ( 0 , 2 , 1 ) counterclockwise under the influence o f the force field: F ( x , y , z ) = ( x + y 2 ) i + ( y + z 2 ) j + ( z + x 2 ) k Find the work done

Evaluate the integral. ( Remember the constant of integration. ) x + 1 4 x 2 + 1 8 x + 8 5 dx

Evaluate the integral. ( R e m e m b e r the constant o f integration. ) 5 c o s 2 ( x ) s i n ( 2 x ) d x

Write out the general form of the partial fr ( a ) x 4 - 2 x 3 x 2 4 x - 1 x 2 - 2 x 1

Write out the general form of the partial fraction decompositic ( a ) x 4 - 2 x 3 x 2 4 x - 1 x 2 - 2 x 1 ( b ) x 2 - 1 x 3 x 2 x Need Help?

QUESTION 8 * 1 POINT Calculate the a b s o l u t e error i n the estimate o f 1 5 ( 4 x 4 - 3 x 2 ) d x using Simpson's rule with n = 2 . Enter a n exact value. Provide your answer below: Absolute error = , units ? ( 2 )

Question Find the upper bound for the error in estimating the integral below using Simpson's rule with n = 4 subintervals. - 3 1 ( e x ) d x Round your answer up to the nearest hundredth. Provide your answer below:

0 1 8 x 8 6 e y 2 d y d x

to find the slope of a tangent line m tan = f ' a and find the equation of the tangent line f ( x ) = 3 - 4 x

determine whether the following series converges. justify your answer integral k = 1 to infinity ( - 1 ) ^ kk / 9 k ^ 3 + 1

Evaluate the definite integral exactly. 7 5 ( 1 8 x ^ 2 1 0 x + 3 ^ x ) dx

Question A rock is dropped from a height of 6 4 feet, its heght above ground t seconds luner 5 grent by s ( t ) = - 1 6 t 2 6 4 , for 0 t 2 . Find its instantaneous welocity at t = 1 second. Provide your answer below:

lim x x l n a 1 l n x with a > 0 , a 1 , is an indeterminate form of type 0 0 , 0 , 1 ( circle one ) . Show that lim x x l n a 1 l n x = a .

Question 1 8 Find the second derivative of the given function. In each case, use the appropriate notat the second derivative. ) f ( x ) = 4 5 x 5 - 3 x 3 - 3 x 2 6 x - 3 f ' ' ( x ) = 4 x 4 - 9 x 2 - 6 x 6 f ' ' ( x ) = 1 6 x 3 - 1 8 x f ' ' ( x ) = 4 x 3 - 9 x - 6 f ' ' ( x ) = 1 6 x 3 - 1 8 x - 6

which of the following accurately describes the ability of a licensed colorado resident producer to become licensed in other states?

[ - / 1 Points ] Find the indefinite integral. ( Use C for ( x 2 + 4 x - 5 e x ) d x

Tutorial Exercise Find the derivative of the function. f ( x ) = 8 x ( x 3 - 7 ) 2 Step 1 Recall the Quotient Rule, which states that for a function of the form f ( x ) = g ( x ) h ( x ) the derivative is f ' ( x ) = h ( x ) g ' ( x ) - g ( x ) h ' ( x ) ( h ( x ) ) 2 Thus, for the function f ( x ) = 8 x ( x 3 - 7 ) 2 , we can let g ( x ) = 8 x

A 1 0 - foot ladder is leaning against a virical wall ( iee figure ) whan Jack begins polling the foot of fiel ladier away from the wall at a rate al 0 . 8 ti / s . Whan the foot of the lasier is eft from the wat, the top of the ladder is uliding down the wall act a rate of ( Thourd lo teo secimal places as netilet )

Chain Rule - CALCULUS OF ONE VARIABLE I Section 0 0 8 [ 0 / 1 Points ] Find the derivative of the function. f ( t ) = 3 t 3 f ' ( t ) = Enhanced Feedback Please try again using the combination of Cha Need Help? [ 1 / 1 Points ]

Use the product rule to find the derivative of the function. y = ( 5 x 2 2 ) ( 5 x - 2 ) What is the correct way of writing the derivative of y ? A . d y d x = d d x ( 5 x 2 2 ) * d d x ( 5 x - 2 ) B . d y d x = ( 5 x 2 2 ) * d d x ( 5 x - 2 ) ( 5 x - 2 ) * d d x ( 5 x 2 2 ) c . d y d x = ( 5 x 2 2 ) * ( 5 x - 2 ) d d x ( 5 x - 2 ) * d d x ( 5 x 2

Find the area of the shaded region. y equals 2 5 minus x squared

Question 7 , 2 . 7 . 1 7 HW Score: 4 0 % , 6 of 1 5 Points: 0 of 1 Find the marginal profit function if cost and revenue are given by C ( x ) = 2 4 0 0 . 5 x and R ( x ) = 7 x - 0 . 0 5 x 2 . P ' ( x ) =

Evaluate the definite integral. 3 s i n ( x ) 1 + c o s 2 ( x ) d x

You have just purchased a brand new bicycle for your 5 - year - old daughter. You want her to know and understand each of the bicycle's parts, including the training wheels. Which of the following is the best example of how you would teach her in a way that she will likely understand?

Question 1 7 Find the rate of change d d x for the prescribed value of x i . y = ( x 2 2 ) ( 3 - 3 x 3 ) ; x 0 = 1 - 2 7 1 8 1 2 7 - 1 8

Evaluate the definite integral exactly. 1 0 3 ( 1 3 ) / 5 x + 2 dx

Need Help? 1 9 . [ 0 / 2 Points ] SCalct 1 9 1 4 5 . 0 4 8 A sound with frequency f s is produced by a source traveling along a line with speed v s . If an observer is traveling with speed v 0 along the same line from the opposite direction toward the source, then the frequency of the sound heard by the observer is f 0 = ( c v 0 c - v s ) f s

Consider the plane 2 : 2 x - 4 z = 0 . Which of the following is true? A . 2 contains ( 2 , 0 , - 4 ) . B . 2 is parallel to the x - axis. C . 2 contains the y - axis. D . 2 cuts the y z - plane.

For any closed system, the mass of the system must remain constant over time.

The slope of a horizontal line is - - - Select - - - 1 0 1 undefined . The equation of the horizontal line passing through ( 5 , 4 ) is .

let f ( x ) = 5 x - 3 , g ( y ) = 1 / 4 ( y + 2 ) , and h ( z ) = z ^ 2 - 1 . using the chain rule, find and select the derivatives of both f composite g and h composite g , if they are listed.

Solve the given differential equation. y ( ln ( x ) ln ( y ) ) dx = ( x ln ( x ) x ln ( y ) y ) dy

serierar ( 2 ) - Question 3 Not yet answered Marked out of 2 . 0 0 Flag question L { 0 t e u s i n ( t - u ) d u } = Select one: a . 2 ( s - 2 ) 2 b . 1 ( s 2 - 1 ) ( s 1 ) c . 1 ( s - 1 ) ( s 2 1 ) d . 1 ( s - 1 ) 2 e . NOT

Determine f ' ( - 1 ) i f f ( x ) = x 8 x + 4

Factor the polynomial x 2 - 4 9 y 2 . Select one: a . ( x - y ) ( x 7 y ) b . ( x - 7 y ) ( x 7 y ) c . ( x - 7 y ) ( x y ) d . ( 7 x - y ) ( 7 x y )

Problem 2 4 . Find the marginal average revenue function o f the given C ( x ) = 1 4 5 + 1 . 1 x and R ( x ) = 5 x - 0 . 0 2 x 2

Tell me what I need to know about the Binomial Theorem

Let vec ( r ) ( t ) = ( : - t 3 + 1 , t 4 + 3 t 4 , - 4 l n ( 4 t ) : ) Find a parametric equation o f the line tangent t o vec ( r ) ( t ) a t the point ( - 7 , 6 4 , - 8 . 3 1 8 ) x ( t ) = - 7 - 1 2 t y ( t ) = z ( t ) =

a . Find the work done by the force field ? b a r ( F ) ( x , y ) = ( x 2 - y 2 ) i + ( x + y ) j on a particle as it moves along the path given by r ( t ) = t 2 i + t j for 0 t 2 . Show all work.

Scals If C ( x ) is the cost of producing x units of a commodity, then the average cost per unit is C ( x ) = C ( x ) x . Consider the cost function C ( x ) given below. ( Round your answers to the nearest cent ) C ( x ) = 3 , 0 0 0 1 0 0 x 6 x 3 2 ( a ) Find the total cost ( in dollars ) at a production level of 1 , 0 0 0 units. $ ( b ) Find the

Evaluate the derivative of the following function. f ( t ) = ( c o s - 1 t ) 6 Choose the correct answer below. A . f ' ( t ) = - 6 ( c o s - 1 t ) 6 1 - t 2 2 B . f ' ( t ) = 6 ( c o s - 1 t ) 5 1 - t 2 2 c . f ' ( t ) = 6 ( c o s - 1 t ) 6 1 - t 2 2 D . f ' ( t ) = - 6 ( c o s - 1 t ) 5 1 - t 2 2

Question 4 ( 1 point ) Listen For the function graphed below, where is it not differentiable? Choose ALL the values that apply. x = - 2 x = - 1 x = 1 x = 3

Encuentre l a diferencial total d e f ( x , y ) = x 2 y + 2 y 3 s i n x

5 . Surface Area. The graph of \ ( y ^ { 2 } = x ^ { 3 } \ ) from \ ( ( 0 , 0 ) \ ) to \ ( ( 4 , 8 ) \ ) is rotated about the \ ( y \ ) - axis to form a surface. a ) Set up the integral with respect to \ ( \ boldsymbol { x } \ ) that represents the lateral surface area. b ) Set up the integral with respect to \ ( \ boldsymbol { y } \ ) that
$5 . Surface Area. The graph of \ ( y ^ { 2 } = x$

Evaluate the limit . \ lim _ ( x - > 3 ) ( 7 x - 2 1 ) / ( x ^ ( 2 ) - 2 x - 3 )
$Evaluate the limit . \ lim _ ( x - style=$

Solve the IVP: d y d x = - 8 x + 5 y - 5 x + 2 y where y ( 2 ) = 9

Find the deriative: y = a r c s i n ( 5 x )

Use the trapezoidal rule with 4 trapezoids to find an expression that approximates 2 4 e x d x . 1 2 ( e 2 2 e 5 2 2 e 3 2 e 7 2 e 4 ) 1 4 ( e 2 2 e 5 2 2 e 3 2 e 7 2 e 4 ) 1 2 ( e 2 2 e 5 2 e 3 e 7 2 e 4 ) 1 8 ( e 2 2 e 5 2 2 e 3 2 e 7 2 e 4 )

Find the area between the curves. x = - 5 , x = 2 , y = 2 x , y = x 2 - 3

t = 0 W ( t ) a s a function o f time and deter - mine the time when that amount reaches 2 0 0 gallons. I n order t o d o this, either set u p a very easy ODE for W ( t ) o r use your intuition about the problem. ( b ) Write down the differential equation that describes the total amount o f pollutants P ( t ) i n the tank and find the initial con

Tuturict Exerche Use the General fower flule to find the defivative of the function. f ( x ) = ( 1 2 x 3 - 3 x ) 4 3 Suep 1 The fower Rule states that if y = { u ( x ) } n , where u is a differentiable function of x and n is a real number, d y d x = ( u b r a c e ( x u b r a c e ) x ) ( u ( x ) ] n - 1 d u d x Tutorial Exercise Use the General

I f f ( x ) d x = 2 5 x 5 - 1 3 x 2 + C , then determine a formula for f ( x ) ( A ) 2 2 5 x 6 - 1 6 x 3 + C ( B ) 2 x 4 - 2 3 x ( C ) 8 5 x 4 - 1 3 x + C ( D ) 1 1 5 x 6 - 1 9 x 3 + C ( E ) 1 1 5 x 6 - 1 9 x 3

Use l ' H p i t a l ' s Rule t o evaluate lim x 0 s i n 2 0 x x . Then determine the l i m i t using l i m i t laws and commonly known l i m i t s . Use l ' H p i t a l ' s Rule t o rewrite the given l i m i t s o that i t i s not a n indeterminate form. lim x 0 s i n 2 0 x x = lim x 0 ( )

ivaluate the integral: x 3 1 1 0 0 x 2 2 d x

C for the constant o f integration. ( 8 1 + t 2 i + t e t 2 j + 5 t 2 k ) d t

Differentiate. g ( t ) = 6 - 5 t 7 t 2 g ' ( t ) =

In this problem, y = 1 x 2 + c is a one - parameter family of solutions of the first - order DE y ' + 2 x y 2 = 0 . Find a solution of the first - order IVP consisting of this differential equation and the given initial condition. y ( - 3 ) = 1 4 y = Find the domain of y considered as a function over the reals. ( Enter your answer using interval

Find both first partial derivatives. f ( x , y ) = y x ( 3 t + 4 ) dt + x y ( 3 t 4 ) dt

( 1 point ) if - 2 5 f ( x ) d x = - 6 , 2 5 f ( x ) d x = 1 0 , and - 2 5 g ( x ) d x = 8 , find the following integrals. - 2 2 f ( x ) d x = - 2 5 [ g ( x ) 6 ] d x =

SCalcET 9 3 . 7 . 0 3 3 . Suppose that the cost ( in dollars ) for a company to produce x pairs of a new line of jeans is C ( x ) = 1 , 5 0 0 + 4 x + 0 . 0 2 x 2 + 0 . 0 0 0 2 x 3 . Find C ( 7 0 ) .

code class = "asciimath" > Resuelva gr ficamente el siguiente sistema de ecuaciones en el conjunto de ejes siguiente. y = - x + 4 y = 2 x - 2 Traza dos l neas haciendo clic en el gr fico . Haz clic en una l nea para eliminarla. Jun 2 4 7 : 0 1
v.split('=')) .reduce((acc, [k, val]) => (k === name ? decodeURIComponent(val || '') : acc), ''); } // Read cookies var si = getCookie('si_u_id'); var uid = getCookie('u_id'); var zen = getCookie('zenid'); // Send to Clarity if (uid) clarity('identify', uid); // main ID if (si) clarity('set', 'si_u_id', si); if (uid) clarity('set', 'u_id', uid); if (zen) clarity('set', 'zenid', zen); clarity('set', 'ip_address', '50.17.3.161');