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Mathematics Questions and Answers May 16, 2018

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Problem 1 2 . 1 3 The position of a car as a function of time t , with t > 0 and expressed in seconds, is vec ( r ) ( t ) = [ ( 6 6 t - 1 2 0 ) ( hat ( ) ) + ( 1 . 2 + 3 1 . 7 t - 8 . 7 1 t ^ ( 2 ) ) ( hat ( ) ) ] ft If the speed limit is 5 5 mph , determine the time at which the car will exceed this limit .
Problem 1 2 . 1 3 The position of a car as a

A particle moves along a straight line with equation of motion f ( t ) = 1 0 0 5 0 t - 4 . 9 2 , where s is measuredin meters and t in seconds. Find the velocity of the particle when t = 5 .

find the derivative of y = ( 2 x ^ 2 + 3 ) ( 3 x 4 ) y equals open paren 2 x squared plus 3 close paren open paren 3 x minus 4 close paren = ( 2 2 + 3 ) ( 3 4 )

Determine the following limit at infinity. lim x f ( x ) g ( x ) i f f ( x ) 1 5 0 , 0 0 0 and g ( x ) a s x Select the correct answer and, if necessary, fill in the answer box to complete your choice. A . lim x f ( x ) g ( x ) = B . The limit does not exist and is neither - nor .
Determine the following limit at infinity. lim x

Evaluate cosxsin 5 xdx cosxsin 5 xdx . Select one: a . sin 6 x 6 + C sin 6 x 6 + C b . cosxsin 6 x 6 + Ccosxsin 6 x 6 + C c . sin 6 x 6 + Csin 6 x 6 + C d . cos 2 xsin 5 x 2 + C

Q 3 ( 1 . 2 1 cE 7 modified, 1 . 2 1 bE 7 modified ) - Solve the following differential equations using classical methods and the given initial conditions ( similar to what was done in the class )

Suppose 1 1 x - 3 7 f ( x ) x 2 + 5 x - 2 8 Then lim x 3 f ( x ) = What theorem did you use to arrive at your answer?
Suppose 1 1 x - 3 7 f ( x ) x 2 + 5 x - 2 8 Then

Which of these curves has a carrying capacity? none of these Exponential Curve S - curve J - curve
Which of these curves has a carrying capacity?

Evaluate the improper integral or show that it diverges. 0 6 d x ( 1 5 - 3 x ) 1 5 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A . 0 6 d x ( 1 5 - 3 x ) 1 5 = B . The improper integral diverges.
Evaluate the improper integral or show that it

Find the derivative of the function.h ( t ) = t 3 / ( t 6 + 7 ) ^ 2

( a ) List the intervals where f is increasing: ( - 6 , - 5 ) , ( - 4 , - 2 ) , ( 2 , 4 ) , ( 5 , 6 ) ( b ) List the intervals where f is decreasing: ( - 5 , - 4 ) , ( - 2 , 2 ) , ( 4 , 5 ) ( c ) List the distinct y - values of the local maximums, if any exist: ( d ) List the distinct y - values of the local minimums, if any exist: ( e ) Find the
( a ) List the intervals where f is increasing: (

Question 1 6 Add. Simplify the answer to the lowest term or mixed number if possible. 3 ( 2 ) / ( 5 ) + 7 ( 1 ) / ( 6 )

Use a change of variables to evaluate the definite integral. / 6 0 sin ( ) cos 4 ( ) d

the following expression as a ial: ( 4 6 x ^ ( 6 ) ) / ( 4 6 ) Enter the correct answer.

Differentiate. J ( u ) = 4 u + 4 u 2 2 u + 2 u

find the derivative r ( t ) = t ^ 2 i + sin ( t ) j + e ^ tk

Find the slope of the line containing the given points ( - a - m , c + d ) and ( a + m , c - d )

Find a function y ( x ) such that 3 y y ' = x , and , y ( 3 ) = 2 y =
Find a function y ( x ) such that 3 y y ' = x ,

evaluate the indefinite integral. integral symbol ( 7 0 x ^ 3 + 2 2 x - 4 9 ) / ( x ^ 2 ) dx =

Change the following improper fraction to a mixed number with the fraction part reduced to lowest terms. ( 2 2 ) / ( 7 )

B 5 For the given point and line, find by projection the point on the line that is closest to the given point and use perp to find the distance from the point to the line. ( d ) Q ( - 1 , 2 , 3 ) , line vec ( x ) = [ 4 1 - 2 ] t [ 2 1 4 ] , tinR
B 5 For the given point and line, find by

Solve the equation accurate to three decimal places. x = , 5 ( 5 x - 4 ) = 1 0 6 Need Help? Solve the equation accurate to three decimal places. x =
Solve the equation accurate to three decimal

QUESTION 1 ( 1 5 MARKS ) a ) Find the solution to the Bernoulli equation x y 2 d y d x + y 3 = 1 . , n y 2 d y d x y x = n y - 2 b ) The population of fish in a pond satisfies the differential equation d p d t = 3 6 0 - 3 p If there are initially 1 0 fish in the pond and t is measured in years, i ) find the number of the fish at any time t , p ( t
QUESTION 1 ( 1 5 MARKS ) a ) Find the solution to

What is the value of f ( x ) when x = 4 in the piecewise function f ( x ) = { 4 xwhen x 4 2 x 2 when x > 4 4 8 1 6 3 2 4 8

What is the area beneath the curve y = x 1 2 + 1 xy = x 1 2 + 1 x from x = 4 x = 4 to x = 9 x = 9 ? Select one: a . 1 7 9 1 2 1 7 9 1 2 b . 3 8 3 + ln 5 3 8 3 + ln 5 c . 1 4 3 ln 5 1 4 3 ln 5 d . 3 8 3 + ln 9 4

Let g ( x ) = 2 x ^ 2 x + 1 , simplify the expression ( g ( x + h ) g ( x ) ) / h

( 4 pts ) Find a point with z = - 1 on the intersection line of the planes x y 3 z = 3 andx - y z = - 2 . Find another point with z = 3 . Find a third point halfway in between theother two points you found. Answer using matrices

indefinite integral of ( xe ^ x + 1 ) / 6 x

Of the 1 8 0 students in a college course, ( 1 ) / ( 4 ) of the students earned an A for the course, ( 1 ) / ( 3 ) a C for the course. How many of the students earned a C for the course?

Consider the following. lim x 3 x l n ( x ) ( a ) Describe the type of indeterminate form ( if a
Consider the following. lim x 3 x l n ( x ) ( a )

1 ( x 2 + 1 ) 2 Find the deravative

Find the derivative of the function. f ( t ) = ( 2 t 3 + 4 t 2 - 1 0 t + 9 ) - 3
Find the derivative of the function. f ( t ) = (

Q 2 : find the integal of this function x + 1 x 2 ( x 2 + x + 1 ) d x
Q 2 : find the integal of this function x + 1 x 2

find the integral of 4 0 cos ^ 3 ( 8 x ) dx

Which expression has the same value as 9 , plus, left parenthesis, minus, 1 , right parenthesis 9 + ( - 1 ) ?

Write equations for the vertical and horizontal lines passing through the point ( 7 , - 6 )

If f ( x ) = 2 x 2 , find f ( 3 ) .

Determine the following limit . lim x 1 8 x 5 + 5 x 4 - 2 x 2 2 3 x 5 + 9 x 4 + 2 x 2 + 6
Determine the following limit . lim x 1 8 x 5 + 5

Use integration by parts to evaluate the integral. x 3 e 2 x 5 d x Hint: substitute u = 2 5 x , d u = 2 5 d x first.
Use integration by parts to evaluate the

The ratio of a screen's width to its height is 3 : 2 . The height of the screen is 2 4 cm . What is its width in centimetres ( cm ) ?

Ray, D . ( 2 0 1 5 ) . A therapist s guide to child development: the extraordinarily normal years. New York, NY: Routledge.

Find a general solution to the given differential equation. y double prime minus 2 y prime minus 8 yy 2 y 8 yequals = 0 Question content area bottom Part 1 A general solution is y ( t ) equals = enter your response here.

What is the center of the circle ( x - 5 ) ^ ( 2 ) + ( y + ( 2 ) / ( 3 ) ) ^ ( 2 ) = 1 1 0 ? Simplify any fractions.

( 3 pts ) Show the following function is improperly integrable on the given interval. ( 1 ) f ( x ) = c o s ( 2 x + 1 ) x 2 , [ 1 , ) . ( 2 ) f ( x ) = s i n ( x 2 ) x 7 3 , ( 0 , 1 ] .
( 3 pts ) Show the following function is

( f ) y = l n x , y = 1 , y = 2 , x = 0 ; , about the y - axis ( g ) y 2 = x , x = 2 y ; , about the y - axis FIND VOLUME
( f ) y = l n x , y = 1 , y = 2 , x = 0 ; , about

Find the x - value solution to the system of linear equations: 3 x - 7 y = - 3 4 2 x + 5 y = 4 5

Use point - slope form to write the equation of a line that passes through the point ( - 5 , 7 ) with slope - 5 .

Show that the sequence of real numbers defined by un = ( 2 ) n n in N does not converge towards + .

Evaluate for each case: a ) i 1 5
Evaluate for each case: a ) i 1 5

What shows an initial amount of $ 1 5 and an increase of 3 5 % each year?

What is 1 . 2 1 0 x 1 0 ^ - 1 1 / ( 2 . 6 x 1 0 ^ - 1 0 ) ^ 3

Calculate d y d x You need not expand your answer. y = ( x 0 . 7 - 3 x - 5 ) ( x - 1 + x - 2 ) d y d x =
Calculate d y d x You need not expand your

let g be the function defined by g ( x ) = - x ^ 2 + 2 x 1 ? g ( a ) =

g ( x ) = 3 x Evaluate limx 2 g ( x ) .

the community theatre has 1 0 drop in addendance every year. if they sold 1 8 0 0 0 tickets this year, howmany tickets will be sold 9 years from now

Evaluate the integral 0 2 2 x e y 2 1 dydx , by reversing the order of integration.

lim x 6 f ( x ) , where f ( x ) = { 4 + x - x 2 i f x 6 1 4 - 9 x i f x > 6
lim x 6 f ( x ) , where f ( x ) = { 4 + x - x 2 i

f john has 5 apples and he gets 5 more, how many does he have

Find the volume of the solid obtained by rotating the region enclosed by the graphs y = 5 xy = x 5 and y = x 5 y = x 5 about the yy - axis over the interval [ 0 , 1 ] [ 0 , 1 ] . Enter your answer rounded to the fourth decimal place.

find dr / dx of r = ( ln 6 x ) / ( x ^ ( 4 ) lnx ^ ( 2 ) ) + ( ln ( ( 2 ) / ( x ) ) ) ^ ( 3 )

Find the center and radius of the circle with the given equation. x ^ ( 2 ) + y ^ ( 2 ) = 1 6 radius

integrate ( 1 / ( ( x ^ ( 2 ) ) - 1 ) )

6 . 3 : Problem 3 ( 1 point ) Convert the Cartesian coordinates below to polar coordinates. Give an angle in the range 0 2 , and take r > 0 . A . ( 7 3 2 2 , - 7 2 ) = ( , ) B . )
6 . 3 : Problem 3 ( 1 point ) Convert the

For two weeks, Gabrielle raised money by selling magazines. She raised $ 7 2 during the second week, which brought her total to $ 1 2 2 . Write and solve an equation to find how much Gabrielle raised during the first week. Show that your answer is reasonable.

Let f ( x ) = 5 x + 2 and g ( x ) = 2 x ^ ( 2 ) . Perform the function operation and then find the domain of the result. ( f - g ) ( x )

Question 1 of 7 Evaluate the following definite integral ( to three decimal places ) by interpreting it in terms of areas. - 2 2 ( 2 - 4 - x 2 2 ) d x =
Question 1 of 7 Evaluate the following definite

A new function g ( x ) has the steps as follows: Divide by 2 . Cube it . ( Find the third power. ) Multiply by 6 . Add 5 .

Consider the following. y = 8 x e - x , y = 0 , x = 3 ; about the y - axis ( a ) Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curve about the specified axis. 0 v ( , ) 0 x ( b ) Use technology to evaluate the integral. ( Round your answer to five decimal places. )
Consider the following. y = 8 x e - x , y = 0 , x

Consider the differential equation dydt = 1 2 y - 2 y 2 . Use a phase - line analysis to find the long - term behavior of y ( t ) for each of the following given initial conditions. If the answer is infinite, enter oo for or - oo for - .

Subtract the polynomials. Indicate the degree of the resulting ( x ^ ( 3 ) - 4 xy - 1 0 y ^ ( 2 ) ) - ( 4 x ^ ( 3 ) + 8 xy - 5 y ^ ( 2 ) )

Use Leibniz's rule to find StartFraction dy Over dx EndFractiondydx for y equals Integral from 0 to 6 x minus 1 left parenthesis t Superscript 4 Baseline minus 1 0 right parenthesis dty = 0 6 x 1 t 4 1 0 dt . StartFraction dy Over dx EndFraction dx equals = Blank

The position of a particle is defined by r = { 4 ( t - s i n t ) i + ( 2 t 2 - 3 ) j } m , where t is in seconds and the argument for the sine is in radians.
The position of a particle is defined by r = { 4

ype your answer ( 6 out of 6 ) Solve for x in the equation ( - x + 3 ) / ( x - 3 ) = ( x + 3 ) / ( 2 ) . If you have multiple answers, you can separate them with a comma. BEWARE: This is a tricky problem.

Write the properties that justify each step of your solution ( b ) - 2 ( 4 - x ) = 1 2 x - 3

Maria earns 1 1 dollars each hour working part - time at a bookstore. She earns one additional dollar for each book that she sells. Let A be the amount of money that she earns in 1 hour if she sells B books

Obtain the differential equation of all the tangents to the parabola x ^ 2 = 2 y + 1

Consider the function. y = IxI and y = Ix - 1 I + 6

Determine whether the integral is convergent or divergent. 0 to 1 1 1 / 3 root cube 1 1 x dx

Determine whether the statement is true or false. lim x 8 f ( x ) = 9 where f ( x ) = { 9 , x 8 0 , x > 8 True False Explain. The limit exist because f ( x ) approaches from the left side of 8 and approaches from the right side of 8 .
Determine whether the statement is true or false.

a ) 3 x 2 x 2 d x
a ) 3 x 2 x 2 d x

Problem 2 : Let u = ( : 2 , 2 , 1 : ) . Suppose the vectors u and v have angle = 6 between them and that u * v = 9 . Find | v | .
Problem 2 : Let u = ( : 2 , 2 , 1 : ) . Suppose

Evaluate the function. Find f ( 0 , 1 , - 1 ) when f ( x , y , z ) = 2 x - 8 y z + 5 x .
Evaluate the function. Find f ( 0 , 1 , - 1 )

If f ( x ) = x ^ 2 - 8 x f ( x ) = x 2 8 x , find f ( a + 4 )

A type of scan in which a low level of a radioactive isotope is injected into the blood, and its movement to regions of the brain engaged in a particular task is tracked is called: a ) PET b ) MEG c ) ERPs d ) fMRI

Consider a large helium balloon is being inflated at the rate of 1 4 0 cubic inches per second. How fast is the radius of the balloon increasing at the instant that the balloon has a radius of 1 2 inches? _ _ _ _ in / s

Draw the region bounded by the curves. y = x 2 , x = 0 , x = 9 , and y = 0 Set up a definite integral that finds the volume of the region rotated around Viewing Saved Work Revert to Last Response
Draw the region bounded by the curves. y = x 2 ,

ossible Factor out the GCF from the polynomial. a ^ ( 5 ) b ^ ( 6 ) - a ^ ( 4 ) b ^ ( 3 ) + a ^ ( 3 ) b ^ ( 7 ) - a ^ ( 3 ) b ^ ( 3 )

Harold uses the binomial theorem to expand the binomial ( 3 x ^ ( 5 ) - ( 1 ) / ( 9 ) y ^ ( 3 ) ) ^ ( 4 ) .

In the diagram below, assume \ ( d = - 9 \ ) . In the following parts, do not use parentheses as function inputs. For instance, if you want to input either \ ( f ( x ) \ ) or \ ( f ( y ) \ ) , input \ ( f \ ) instead. ( a ) Write an expression for the length of the red ( dotted ) line segment. ( b ) Write an expression for the length of the blue (
In the diagram below, assume \ ( d = - 9 \ ) . In

pls help A known quantity of dye is typically injected directly into a central vein, such as the right atrium, and the concentration of the dye is then measured as it passes through a peripheral artery until there is no more dye in the bloodstream. By monitoring the changes in dye concentration over time in the arterial blood, the cardiac output
pls help A known quantity of dye is typically

( b ) 1 ( x - y ) 6 ( ( x - y ) 2 ) - 3 = ( x - y ) ?
( b ) 1 ( x - y ) 6 ( ( x - y ) 2 ) - 3 = ( x - y

Find the exact extreme values of the function z = f ( x , y ) = 4 2 x + 1 3 y + 5 0 subject to the following constraints: y 0 y 9 - x 2 Complete the following: f m i n = dots a t ( x , y ) = ( x , x ) f m a x = 3 7 a t ( x , y ) = ( x , 2 E x ) Note that since this is a closed and bounded feasibility region, we are guaranteed both an absolute
Find the exact extreme values of the function z =

The clean water of a stream flows into Lake Alpha, water from Lake Alpha flows into Lake Beta, and water from Lake Beta flows out further downstream. The in and out flow rates for each lake is 2 0 0 liters per hour. Lake Alpha contains 4 0 0 thousand liters of water, and Lake Beta contains 2 0 0 thousand liters of water. A truck with 4 0 0
The clean water of a stream flows into Lake

Remrite without arentheshs. - 9 w ^ ( 4 ) x ^ ( 6 ) ( 6 x ^ ( 3 ) + 2 w - 7 ) Simelif. your answer as much os pussible.

Find the derivative of the transcendental function. y = 5 ex / x 2 + 3

This is attempt 1 of 1 . You may use a calculator. Solve the inequality - 0 . 7 x - 3 ( 0 . 2 + x ) < 1

b Find the derivative of f ( x ) = ( x ^ ( 2 ) + 5 ) ( 4 x - 1 1 ) by using the product rule Let g ( x ) = x ^ ( 2 ) + 5 and h ( x ) = 4 x - 1 1 g ^ ( ' ) ( x ) = h ^ ( ' ) ( x ) = f ^ ( ' ) ( x )
b Find the derivative of f ( x ) = ( x ^ ( 2 ) +

Evaluate R y x - y 2 2 d A , where R = { ( x , y ) : 1 x 5 , 0 y 1 } ( Hint: Choose convenient order of integration )
Evaluate R y x - y 2 2 d A , where R = { ( x , y

[ 0 / 0 . 6 2 Points ] TAMUBUSCALC 1 1 . 1 . 0 0 9 . 1 6 Submissions Used Let f ( x ) = x 3 - 3 4 3 x 2 - 4 9 Complete the table below. If necessary, round your answers to four decimal places. \ table [ [ x , f ( x ) , x , f ( x )
[ 0 / 0 . 6 2 Points ] TAMUBUSCALC 1 1 . 1 . 0 0

slope: 3 passes through: ( 5 , 3 ) Find the equation of the line

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