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mathematics
june 2018
23

Mathematics Questions and Answers June 23, 2018

Expert-verified solutions to help you succeed

The concentration C ( t ) of a certain drug in the bloodstream after t minutes is given by the formula C ( t ) = 0 . 0 2 ( 1 - e ^ - 0 . 2 t ) . What is the concentration after 4 minutes?

Find the average rate of change of the function f ( x ) = 6 3 x 6 , on the interval zin [ - 4 , 3 ] . Average rate of change = Give an exact answer.

Step 3 y = - 5 4 * x + 5 m = b = 1

the function f ( x ) = ( 2 ln ( x ) + 1 ) / ( ln ( x ) 3 ) . ( a ) By clearly showing your step - by - step operations, find f ^ 1 ( x ) . ( b ) Find the domain and range of f ( x )

EXAMPLE 5 Evaluate the limit below. lim h 6 ( 7 + h ) 2 - 4 9 h SOLUTION If we define F ( h ) = ( ( 7 + h ) 2 - h ) then we can't compute the limit by letting h = 0 since F ( 0 ) is undefined, but If we simplify F ( h ) algebraically, we find that F ( h ) = ( u b r a c e ( - h u b r a c e ) ) h = ( Recall that we consider only h = 0 when letting h

[ 0 / 1 Points ] LARCALC 1 1 1 1 . 1 . 0 5 5 . Find the component form of u v given the lengths of u and v and the angles that u and v make with the positive x - axis. | | u | | = 5 , u = 9 | | v | | = 1 , v = 5 u v = Need Help? Viewing Saved Work Revert to Last Response Question 8 of 1 2

Find the y - intercept of the line. y = - 0 . 6 x 4 . 7

Find the average rate of change of the function over the given interval. f ( x ) = x 2 9 x , [ 1 , 3 ] f x =

code class = "asciimath" > Application ( 2 8 Marks ) Solve the following equations ( 1 6 marks ) ( a ) 3 tan 2 x - 1 = 0 , [ - \ pi , \ pi ] ( b ) cosx ^ ( 2 ) - 3 sinx ^ ( 2 ) = 1 , [ - 2 \ pi , 2 \ pi ] ( c ) cos ( x - ( \ pi ) / ( 3 ) ) = cos ( x + ( \ pi ) / ( 3 ) ) - 1 , [ 0 , 2 \ pi ]

Determine the infinite limit . lim x 9 x 2 9 xx 2 1 8 x + 8 1

( 3 . 3 ) The line integral C x y 4 d s where C i s the half - right circle o f x 2 + y 2 = 1 6 equals

Solve the initial value problem 4 + 2 3 = 1 1 t 4 dydt + 2 t 3 y = t 1 1 with > 0 t > 0 and ( 1 ) = 0 y ( 1 ) = 0 .

Question 6 . Use a ) the left end, b ) the right end and c ) the traperacidal rules to approximate the definite integral 1 ( x 2 1 ) d x using a partition of - 1 . 1 into 4 equal parts.

Evaluate the limit . Give your answer in exact form. If the limit does not exist, enter DNE. lim h 0 s i n ( 8 h ) 3 h = Justify your answer. The limit does not exist bocause lim h 0 s i n ( 8 h ) 3 h = . The limit exists because lim h 0 s i n ( 8 h ) 3 h = L , where L is a real number. The limit does not exist because lim h 0 s i n ( 8 h ) 3 h is

Find the value of b for which the differential equation ( y e 8 x y x ) d x ( b x e 8 x y ) d y = 0 is exact, then solve it using that value of b . The differential equation is exact only when b = - The general solution, in implicit form, is = c , for any constant c . NOTE: Do not enter an arbitrary constant or any constant lerm.

a . Evaluate x x 8 2 d x using integration by parts. b . Evaluate x x 8 2 d x using substitution. c . Verify that your answers to parts ( a ) and ( b ) are consistent. a . Use the integration by parts formula. Choose the correct answer. A . 2 x x 8 2 2 x 8 2 d x B . 2 x x 8 2 - 2 x 8 2 d x C . 2 x x 8 2 2 x 8 2 d x D . 2 x x 8 2 - 2 x 8 2 d x

For the vectors u = ( : 1 , 3 , 2 : ) and v = ( : 0 , 3 , 1 : ) , evaluate the following expressions. a . 2 u 4 v b . 3 u - v c . | u 4 v | a . 2 u 4 v = ,

( 6 p t s ) 3 ) Evaluate the integral d x 4 x 2 2 5 2

What is the derivative of g ( x ) = x 4 e - x . Do not include " g ' ( x ) = " in your answer.

Find the l i m i t o f f ( x ) = 9 x - 1 1 a s x approaches and a s x approaches - . lim x f ( x ) = - 1 1 ( T y p e a simplified fraction. ) lim x - f ( x ) = 1 ( T y p e a simplified fraction. )

Differentiate. g ( x ) = 6 x - 5 9 x 8 x 3 g ' ( x ) =

At least one of the answers above is NOT correct. Solve the separable differential equation for u d u d t = e 4 o 7 t using separation of variables given the inital condition u ( 0 ) = - 1 2 . First, we must write it in the standard form t d t = g ( t ) * h ( u ) , which is: d u d t = , - e 4 u , help ( f o r m u l a s ) Now, separate the

C for the constant o f integration. ( s e c 2 ( t ) i + t ( t 2 + 1 ) 4 j + t 6 l n ( t ) k ) d t

A particle moves along a path given by vec ( r ) ( t ) = ( : 4 c o s t , 4 s i n t , 3 t : ) . Sketch the curve using the interval tin [ 0 , 4 ] , or tin [ - 2 , 2 ]

Complete the table below giving the amount P that must be invested at interest rate 8 . 5 % compounded continuously to obtain a balance of A = $ 2 0 0 0 0 0 in t years. tP 1 1 0 2 0 3 0 4 0 5 0

Find the limit . lim x - x x 2 - 6 6 x 5 x 2 2 x 3

Evaluate the integral. ( Use C 5 s i n 3 ( x 2 ) x 2 d x

Find the solution of the differential equation which satisfies the initial condition y ( 1 ) = e ^ 2 . ( ( ln ( y ) ) ^ 4 dy / dx = x ^ 4 y

d y d x = - d e l F d e l x d e l F d e l y = - F x F y use the follwing formula t o solve this question. t a n - 1 ( x 2 y ) = x + x y 2

QUESTION 1 8 1 POINT Evaluate lim x 0 ( 6 x + 9 ) 2 - 8 1 - 6 x Submit an exact answer. Provide your answer below:

code class = "asciimath" > Calculate the instantaneous rate of change of f ( x ) with respect to x at the given value of x . a . f ( x ) = 5 - x ^ ( 2 ) , x = 2 b . f ( x ) = ( 3 ) / ( x ) , x = ( 1 ) / ( 2 )

assume a person burns 2 0 calories per day per pound of body weight. solve this differential equation, if the person starts out weighing 1 7 0 pounds and consumers 3 8 0 0 calories a day

i n relation t o linear algebra, please show work. explanation welcome but please show work Show all images Show all images Show all images done loading

Determine if the equation specifies a function with independent variable x . If it does find the domain. If it does not finds a value for x to which. X ^ 2 + y ^ 2 = 1 0 0

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

find the integral of dx / ( x ^ 2 - 1 ) ^ 3 / 2 taken from 2 to 5

g ( x ) = x + 8 ( x 1 ) 3 2 log ( x 2 ) 2 if x < 1 if 1 x < 4 if x 4 What is the limit as x approaches 4 ^ -

domain of ( f g ) ( x ) f ( x ) = 2 / x , g ( x ) = x ^ 2 - 9

g ( x ) = 3 x + 7 a ) Find the average rate of change of the function between x = a and x = b . ( b ) Find the slope of the line.

y = a Prove that d y d x = y 2 l o g y ? x ( 1 - y ) l o g x

Evaluate 1 ( x 4 ) 5 dx . Evaluate 1 ( x 4 ) 5 dx . 1 4 ( x 4 ) 4 + c 1 4 ( x 4 ) 4 + c 1 5 ( x 4 ) 4 + c 1 5 ( x 4 ) 4 + c 1 6 ( x 4 ) 6 + c 1 6 ( x 4 ) 6 + c 1 ( 1 / 6 ) ( x 4 ) 6 + c 1 ( 1 / 6 ) ( x 4 ) 6 + c

Consider the series. ( 8 3 ) + ( 8 3 ) 2 + ( 8 3 ) 3 + ( 8 3 ) 4 + . . . This series can b e written a s genometric series i n the form n = 0 c r n . Identify c and r i n the geometric series. ( G i v e exact answers. Use symbolic notation and fractions where needed. )

Enter a T or an F in each answer space below to indicate whether the corresponding statement is true or false, the answers correct to receive credit. lim x 1 x 2 7 x - 1 8 x 2 6 x - 1 6 = lim x 2 x 2 7 x - 1 8 lim x 2 x 2 6 x - 1 6 If lim x f | f ( x ) g ( x ) | exists, then the limit is f ( 7 ) g ( 7 ) If lim x 6 f ( x ) = and lim x 6 g ( x ) = ,

solve the initial value problem y ' ( x ^ 2 + 2 ) + 4 x ( y ^ 2 + 2 y + 1 ) = 0 y ( 1 ) = - 1

area between the curve of 2 * cos ( x / 4 ) and y = x / 2 bounded by 0 to 6 * pi

Find the general solution for the first - order differential equation. StartFraction dy Over dx EndFraction equals negative 9 xdydx = 9 x

Find the derivative of f ( x ) = e x - x 3 l n ( x ) f ' ( x ) = e x - 3 x 2 1 x f ' ( x ) = x e - x 3 l n ( x ) f ' ( x ) = e x - 3 x 2 l n ( x ) f ' ( x ) = e x - x 3 1 x

Question 7 A complete list of the regular singular points for the differential funstion x ( x 1 ) ? 2 ( x 2 ) 2 ( x - 2 ) 4 y ' ' - ( x - 1 ) ( x - 2 ) 3 y ' x ( x - 2 ) y = 0 is siven by: - 1 , 0 , 1 1 , - 2 0 , 1 0 , 2 0 , 1 , 2

code class = "asciimath" > A . Solve for the members marked bv X . B . Solve for Moments M _ ( A ) & M _ ( E ) , and reactions at B , D and E . ( Three Moment Equation ) C . Solve for the slope and angle. ( Double Integration Method )
$code class = "asciimath" style="width: 25%; display: block; margin-left: 0; margin-right: auto;"></a></div> </h2> </div> </div> <div class="related-question-statment col-md-12 col-lg-12"> <div class="no-padding question-statement-complete-placement"> <h2 class="small_h2"> <a href="/study-help/questions/write-the-equation-of-the-sphere-in-standard-form-x-28249352" class="related-question-statement-styling">Write the equation of the sphere in standard form. x 2 + y 2 + z 2 + 1 2 x 8 y + 6 z + 5 2 = 0 Find its center and radius. center ( x , y , z ) = radius</a> </h2> </div> </div> <div class="related-question-statment col-md-12 col-lg-12"> <div class="no-padding question-statement-complete-placement"> <h2 class="small_h2"> <a href="/study-help/questions/verify-whether-the-following-ode-i-s-exact-and-find-28249354" class="related-question-statement-styling">Verify whether the following ODE i s exact and find its general solutions. ( 1 + e x y + x e x y ) d x + ( x e x + 2 ) d y = 0</a><div class="questionHolder"><a href="/study-help/questions/verify-whether-the-following-ode-i-s-exact-and-find-28249354"><img src="https://dsd5zvtm8ll6.cloudfront.net/si.experts.images/questions/2025/09/68bb7b40cc41a_24868bb7b40421e4.jpg" alt="Verify whether the following ODE i s exact and" class="sc-95ce458d-1 gwnYMC" style="width: 25%; display: block; margin-left: 0; margin-right: auto;"></a></div> </h2> </div> </div> <div class="related-question-statment col-md-12 col-lg-12"> <div class="no-padding question-statement-complete-placement"> <h2 class="small_h2"> <a href="/study-help/questions/consider-the-surface-in-r-3-given-by-z-28249355" class="related-question-statement-styling">Consider the surface in R 3 given by z = 1 6 x 2 y 2 . ( a ) What is the range of z for this surface? Enter your answer as an interval using interval notation. For example [ - 3 , 2 ) for the interval - 3 z 2 . If you need to enter infinity, you can either copy and paste the symbol or type infinity Answer: ( b ) The equation of the level curve for</a><div class="questionHolder"><a href="/study-help/questions/consider-the-surface-in-r-3-given-by-z-28249355"><img src="https://dsd5zvtm8ll6.cloudfront.net/si.experts.images/questions/2025/09/68bb7b40d0a15_24868bb7b4042a17.jpg" alt="Consider the surface in R 3 given by z = 1 6 x 2" class="sc-95ce458d-1 gwnYMC" style="width: 25%; display: block; margin-left: 0; margin-right: auto;"></a></div> </h2> </div> </div> <div class="related-question-statment col-md-12 col-lg-12"> <div class="no-padding question-statement-complete-placement"> <h2 class="small_h2"> <a href="/study-help/questions/let-a-b-e-a-real-number-w-e-define-28249356" class="related-question-statement-styling">Let a b e a real number. W e define a function f ( x ) = { e x - a - 1 i f x 3 x 2 + 8 i f x 3 Find the value o f a such that the l i m i t lim x 3 f ( x ) exists. FORMATTING: Give a n exact answer. I n Mobius, l n ( x ) i s simply written l n ( x ) . Answer: a =</a><div class="questionHolder"><a href="/study-help/questions/let-a-b-e-a-real-number-w-e-define-28249356"><img src="https://dsd5zvtm8ll6.cloudfront.net/si.experts.images/questions/2025/09/68bb7b40be57c_24868bb7b403f927.jpg" alt="Let a b e a real number. W e define a function f" class="sc-95ce458d-1 gwnYMC" style="width: 25%; display: block; margin-left: 0; margin-right: auto;"></a></div> </h2> </div> </div> <div class="related-question-statment col-md-12 col-lg-12"> <div class="no-padding question-statement-complete-placement"> <h2 class="small_h2"> <a href="/study-help/questions/evaluate-the-limit-if-it-exists-lim-x-4-28249357" class="related-question-statement-styling">Evaluate the limit , if it exists. lim x 4 x 2 4 xx 2 3 x 4</a> </h2> </div> </div> <div class="related-question-statment col-md-12 col-lg-12"> <div class="no-padding question-statement-complete-placement"> <h2 class="small_h2"> <a href="/study-help/questions/jules-7-and-8-1-5-of-1-6-28249362" class="related-question-statement-styling">Jules 7 and 8 ) 1 5 of 1 6 This teate 6 4 poinely This questions 6 pc . Find the area of the region bounded by the curves y = x 3 and y = 5 x 2 between their intersections. The area of the region is square unitis ) . ( Simplify your answer. Type an integer or a fraction )</a><div class="questionHolder"><a href="/study-help/questions/jules-7-and-8-1-5-of-1-6-28249362"><img src="https://dsd5zvtm8ll6.cloudfront.net/si.experts.images/questions/2025/09/68bb7b413a169_24868bb7b40b273d.jpg" alt="Jules 7 and 8 ) 1 5 of 1 6 This teate 6 4 poinely" class="sc-95ce458d-1 gwnYMC" style="width: 25%; display: block; margin-left: 0; margin-right: auto;"></a></div> </h2> </div> </div> <div class="related-question-statment col-md-12 col-lg-12"> <div class="no-padding question-statement-complete-placement"> <h2 class="small_h2"> <a href="/study-help/questions/0-1-points-larcalca-2-2-28249365" class="related-question-statement-styling">[ 0 / 1 Points ] LARCALCA 2 2 . 2 . Find the derivative of the function. f ( x ) = x 2 - 7 x 3 f$

\ table [ [ a ) , Evaluate the definite integral: ] , [ , 1 3 ( x 2 - 4 x 3 ) d x
$\ table [ [ a ) , Evaluate the definite integral:$

Assignment Scoring Your last submissich i s used for your score. 7 . [ 0 1 Points ] DETAILS M Y NOTES LARC Find the volume o f the solid generated b y revolving the r e y = 1 7 x + 6 2 y = 0 x = 0 x = 5 Need Help?

Find all the first and second order partial derivatives o f f ( x , y ) = - 6 s i n ( 2 x + y ) + 9 c o s ( x - y ) . A . d e l f d e l x = f x = B . d e l f d e l y = f y = C . d e l 2 f d e l x 2 = f = D . d e l 2 f d e l y 2 = f y y = E . d e l 2 f d e l x d e l y = f y x = F . d e l 2 f d e l y d e l x = f x y =

Use series to evaluate the limit . lim x 0 ( sqrt ( 1 + x ) 1 1 / 2 x ) / x 2

For w = f ( x , y , z ) where x = g ( r , s ) , y = h ( r , s , t ) , and z = p ( r , t ) , find a n expression for d e l w d e l t .

Use an appropriate substitution to solve the equation and find the solution that satisfies y ( 1 ) = 1 . y ' - ( 6 / x ) y = y ^ 4 / x ^ 6

iven the second - order, linear, homogeneous differential equation y - 1 0 y + 2 5 y = 0 and the functions y 1 ( x ) = e 5 x y 2 ( x ) = x e 5 x ( a ) Verify that y 1 ( x ) and y 2 ( x ) are solutions t o the given differential equation. ( b ) Verify that y 1 ( x ) and y 2 ( x ) are linearly independent using the Wronskian. ( c ) y 1 ( x ) and y 2

Given the following, vec ( u ) = [ 3 , - 1 , 4 ] , vec ( v ) = [ 6 , - 4 , - 8 ] , and vec ( w ) = [ 7 , - 3 , 4 ] . Are the vectors vec ( u ) , vec ( v ) , and vec ( w ) coplanar? [ 4 T ] PART D - Application 2 3 . Given the points A ( - 5 , 1 , 3 ) , B ( 2 , 7 , - 1 ) , and C ( 5 , 5 , 6 ) . Determine the area of ? ? ? ? A B C . [ 4 A ] 2 4 . A

Q 4 . Obtain y ( 1 . 5 ) b y solving the following ordinary differential equation using Heun's method. Step size = 0 . 5 0 and initial conditions: y ( 1 ) = 2 d y d x - 3 x + 2 y x = 0 Q 5 . Determine the following integral b y applying the Simpson's 1 3 rule twice. 0 4 x c o s ( x ) d x

Taban yar ap 6 br , y ksekligi 3 6 br olan dik dairesel koni, tepesinden y br uzaktan, taban na paralel bir d zlemle kesiliyor. Elde edilen dairesel kesitin alammn ortalama degeri nedir? I. 1 6 3 II . 4 9 3 III. 2 5 3 IV . 6 4 3 V . 1 2

Let lim x 6 f ( x ) = 7 and lim x 6 g ( x ) = 3 . Use the limit rules to find the following limit . lim x 6 f ( x ) g ( x ) 6 g ( x ) lim x 6 f ( x ) g ( x ) 6 g ( x ) = ( Type an integer or a simplified fraction. )

Question 1 Find the partition number ( s ) of R ( x ) = 1 6 ( x 3 ) x 2 ( x 2 - 4 ) Choose all that apply. - 3 - 1 6 2

Evaluate the derivative o f y = 9 x + 7 x 2 + 7 x + 8 a t x = - 1 .

Use the Product Rule to find the derivative of the function. f ( x ) = ( 3 x - x 3 ) ( 8 x 5 ) f ' ( x ) =

Given f ( x ) = 1 5 x 2 s i n x 9 x - 7 , find f ' ( x ) f ' ( x ) =

e . d 2 y d t 2 = 3 2 e - 4 t ; y ( 0 ) = 1 , y ' ' ( 0 ) = 0

Suppose that f ( x , y ) = x 3 y 2 . The directional derivative of f ( x , y ) in the direction - 2 , 1 and at the point ( x , y ) = ( - 1 , - 3 ) is

d { 4 - 2 n } n = 1 [ 5 Marks ] i i . { n 2 + 1 2 n 2 + 3 } n = 1

Solve the following initial value problem: 2 dy dt + y = 4 t with y ( 0 ) = 9

Which of the following fractions is the largest? a . 3 5 b . 9 8 c . 6 1 1 d . 7 1 9 Mark to review later...
$Which of the following fractions is the largest?$

Use a ( , ) - proof t o justify the given l i m i t .

Solve. Round to the nearest hundredth if necessary. Find the weight in kilograms of a 1 7 5 - pound person.

integral: 0 4 1 sin 4 x + cos 4 xdxintegral from 0 to the fraction with numerator pi and denominator 4 end - fraction of the fraction with numerator 1 and denominator the fourth power of sine x plus the fourth power of cosine x end - fraction d x 4 0 1 sin 4 + cos 4

Find the derivatives of the following functions. g ( x ) = 2 x 3 7 x 2 + 7 f ( x ) = ( 2 x 3 7 x 2 + 7 ) 5

Identify the variables i n the following parametric equations modeling projectile motion: x = 2 5 c o s 7 0 t y = 2 5 s i n 7 0 t - 1 6 t 2 + 1 0 angle projectile i s launched a t initial height projectile i s launched from initial velocity o f projectile

S e t i i n i z cevab n i a r e t l e n d i i n i g r e n e kadar bekleyiniz. Soruyu b o b r a k m a k isterseniz i a r e t l e d i i n i z s e e n e e tekrar t k l a y n z . 8 ( - 1 ) n n 2 n 2 - 6 n 4 n 4 ( - 1 ) n n 2 n 2 - 6 n 4 n 4 0 8 ( - 1 ) n n 2 n 2 - 6 n 2 n 2

Decide from the gaph whether a limit ecists. If a limit ecists, find its value. l m x - 1 F ( x ) What is the link? Select the correct choice below and fill in any answer boses in your choice. A . The lind is the real number R . The ling flows not eedit

L - 1 [ 4 s 3 ( s 3 + s 2 ) ( s 2 + 5 ) ]

k M gfEU 3 2 r 9 0 1 0 9 FpRLqEEQ Final Exam Find the value of y where the given function has a horizontal asymptote. If one does not exist, type "none". f ( x ) = 2 x - 2 3 x 4 y =

It will be turned in automatically after the due date. - 5 0 ( 2 x - 5 ) d x a ) Find a formula to approximate the above integral using n subintervals and using Midpoint Rule. ( enter a formula involving n alone ) . b ) Evalute the formula using the indicated n values. n = 1 0 n = 1 0 0 n = 1 0 0 0 c ) Find the limit of the formula, as n , to find

A ball of radius r is cut into three pieces by parallel planes at a distance of r / 3 on each side of the center. Find the volume of the middle piece

find the slope o f the curve a t the point indicated y = x - 5 x + 5 x = 1

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