Application of derivatives Questions and Answers

Write the first five terms of the arithmetic sequence a 7 d 2 OA 7 8 9 10 11 OB 9 11 13 15 17 OC 0 7 9 11 13 OD 7 9 11 13 15

Find the slant asymptote if any of the graph of the rational function g x x 3 2 X 36 A y x OB y x 3 OC y x 36 OD no slant asymptote

A salesperson gets a commission of 1 200 for the first 10 000 of sales and then 600 for each additional 10 000 or partial of sales Let S x represent the commission on x dollars of sales Find the value of S 95 0 OA 5 700 O B 6 300 O C 6 900 OD 6 600

Given functions f and g find f g f x 6x 2 g x 9x 7 OA 3x 5 OB 15x 9 OC 3x 9 OD 3x 5

List the intervals on which the function is increasing the intervals on which it is decreasing and the location of all local extrema Ay A 2 Q List the open interval s on which the function is increasing Select the correct choice below and if necessary fill in the answer box to complete your choice OA The function is increasing on the interval s Type your answer in interval notation Use a comma to separate answers as needed OB The function is never increasing List the open interval s on which the function is decreasing Select the correct choice below and if necessary fill in the answer box to complete your choice OA The function is decreasing on the interval s Type your answer in interval notation Use a comma to separate answers as needed OB The function is never decreasing Identify any local extrema Select the correct answer below and if necessary fill in any answer box es within your choice OA There is no local maximum and the local minimum minima occur s at x Use a comma to separate answers as needed OB There is no local minimum and the local maximum maxima occur s at x Use a comma to separate answers as needed OC There is are local maximum maxima at x at x Use a comma to separate answers as needed OD The function has no local extrema and there is are local minimum minima

Find the location of the absolute maximum and absolute minimum of the function on the interval 6 0 The absolute maximum occurs at x Use a comma to separate answers as needed The absolute minimum occurs at x Use a comma to separate answers as needed Af x A

2 Find cos 0 sin 0 de moyur in to enroldeig nivollol edy to lis od ar 10 mq dto vas mol glid on wison 1 I talt bartition 1 tuonsob zid gaingie

a Find the third degree Maclaurin polynomial for f x 6 Solve b Use your answer above to approximate the cos 1 sin 1

9 Find an equation tangent to the curve at the point when t 4 and at 13 y 5t bail

1 Find x e dx

11 Find dx dt dy dt and dy dx where x 2et y t cost adl of caston PAUZ

Assignment 3 5 points Consider the following linear optimization problem min I1 312 s t 221 213 12 13 313 12 21 21 T2 13 I1 I4 TA 14 13 24 8220 C4 a Reformulate the problem in standard form b Introduce slack variables and give the dictionary with the slack variables in the basis Does this dicti

Match each function with its graph Function f x f x f x Graph Color a blue b green c red

2 Use implicit differentiation to find an equation of the tangent line to the curve at the given point M X X J sin 3x xcos 3y 7 y 36 A 9

For the rectangular coordinates 3 1 a plot the point and b give two pairs of polar coordinates for the point where 0 0 360 a Choose the correct plot of 3 1 below A B Ay Ay C Ay OD Ay Q b Give two pairs of polar coordinates for the point where 0 0 360 Type an ordered pair Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Type your answer in degrees Do not include the degree symbol in your answer Use a comma to separate answers as needed

Divide Write your answer in fraction form 21 5x 11x 9 x 1

The following graph shows the average candy Consumption of a town in thousands of pounds per year n selected years Estimate the total candy consumption from 2001 to 2006 using rectangles of width 1 year and height determined by the value of the function at the left endpoint Pounds of candy consumed in thousands 0 2000 2002 2004 2006 2008 2010 Year Q The approximate total candy consumption of th town from 2001 to 2006 was thousand pour of candy Simplify your answer Type a whole number

Write the complex number 4 4 3i in trigonometric form where r is exact and 0 0 2 Select the correct choice below and fill in the answer boxes to complete your choice Simplify your answer Use integers or fractions for any numbers in the expression Type any angle measures in radians Type exact answers using as needed OA 4 4 3i sin i cos OB 4 4 3i COS isin

r 10 csc 0 Choose the rectangular equation that is equivalent to r 10 csc 0 A y 10 OB C x 10 D y 10x 10y Choose the correct graph of the equation below O A B Q 5 O C Q OD 46

Find the quotient 3x 6 cos i sin 2 T 3 3 cos i sin 2 6 cos i sin 2 3 cos 3x 2 172 I 2 i sin 2 BIN in rectangular form using exact values Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Type answer in the form a bi

Find the resultant sum of the pair of complex numbers Express your answer in rectangular form Do not use calculator 4 5i 1 3i The sum is Type your answer in the form a bi

The acceleration of an object in m s is given by the function a t 4 sin t The initial velocity of the object is v 0 1 m s a Find an equation v t for the object velocity v t b Find the object s displacement in meters from time 0 to time 3 meters c Find the total distance traveled by the object from time 0 to time 3 meters

10 For what value of k will the vectors a 4 12 16 b 7 5 2 and c 2 7 k be coplanar

9 Determine the value s of z such that the points A 1 5 8 B 0 9 4 and C 8 5 z form an Isosceles triangle where AC is the base i e the non equal side

6 Write 5 7 as a linear combination of 2 3 and 1 4 Leave your answers as fractions where applicable

For the vectors u 5 8 and v 4 6 a Write u in terms of i and j b Determine lvl

6 12 oldu una g re tan2a nin de eri k tana

6 log 8 log 7 log 9 I leminin sonucu ka t r What is the result of The transaction

1 log 42 log 42 log427 i leminin sonucu ka t r what is the result of the transaction

log log x 1 1 oldu una g re x ke ir Since what is X

Use the trapezoidal rule with n 5 to approximate 6x dx and use the fundamental theorem of calculus to find the exact value of definite integral The approximate value of the integral from the trapezoidal rule is Simplify your answer The exact value of the definite integral is Simplify your answer

Evaluate 4 S 4 S 50 4 dt 5 t dt 5 t 4 Type an exact answer

7 In the creation of a DNA profile a b C d minisatellites short tandem repeats introns exons are typically use

Consider the function f t 4 sec t 2t Let F t be the antiderivative of f t with F 0 0 Then F 5

Find the derivative of 2e 92 cos 6x Hint use product rule and chain rule Use e x for e 12e 9x Y 9x sin 6x 18e cos 6x Now find the equation of the tangent line to the curve at X 0 Write your answer in ma b format

Q what are the bounds of integration for the first integral and a f x da f x dx f a da f x dx F x dx f x dx 5

Consider the function f t 6 sec t 9t Let F t be the antiderivative of f t with F 0 0 Then F 2

5 If x 2t t and y 6 2t find an equation of the tangent in terms of x and y to e curve at t 2

Find the sum of the first 9 terms of the following geometric sequence 8 16 32 64 128 OA 4 090 OB 4 068 OC 4 125 OD 4 088

2 Rewrite as one single logarithm with coefficient 1 4 points log 2y 5 2 log y 3

F 2x 12x x 4x 12 3 4 8x 24x x 9x 18

A C x2 5x 6 x 3x x 2x x 2x 1 X 3 x 4x 3 x 3x B D y2 7y 1 y 8y 7 x 2x 3x 2x x 2 x 1

Find the derivative of the function g x g x et 2 et 5 2x

Find the area bounded by y 2x3 54x 135 the x axis and the first coordinates of the relative maximum and minimum values of the function The area is

Use the fact that the derivative gives the slope of a curve to decide which of the graphs A F in the figure below could represent a solution to the differential equation A C E 6x B xe LV D H F XA y I

Find the Taylor series for f x sin a centered at a 11 kla

1 Find the Taylor series for f x sin x centered at a KIN

A motorcyclist being monitored by radar accelerates at a constant rate from 0 mph v 0 0 to 55 mph in 15 sec How far has the motorcycle traveled after 15 sec Hint Convert seconds to hours After 15 sec the motorcycle has traveled mi Simplify your answer Type an integer or a fraction

Does n 1 n 5 converge or n 10n 9 2 diverge 16

The graph shows the function y w t 1 5 4 3 2 7 1 2 3 4 5 We define a new function a z X 0 1 2 3 1 Complete the table of values for the function a a x 4 2 5 4 15 6 w t dt