Differentiation Questions and Answers

Determine the derivative of h t 3 cos t 4 sin t L A

Find the general solution using the power series 21

Consider the function in the graph to the right The domain of the function is 3 3 X The range of the function is 00 00 The function is increasing on the interval s 1 0 7 X The function is decreasing on the interval s 3 1 X 5 4 3 2 1 3 2 3 0 7 0 3 1 1 0 52 2 1 2 3 4 5

Find the real zeros of f Use the real zeros to factor f f x x 12x 34x 16 The real zero s of f is are 8 2 2 2 2 Simplify your answer Type an exact answer using radicals as needed Use integers or fractions for any numb the expression Use a comma to separate answers as needed Factor f f x Factor completely Type an exact answer using radicals as needed Use integers or fractions for any numbers

111 dt kW c Professor Lafleure a new p Lewiston area During hi is proportional to the squar increases by 2000 per meter is located at an altitude of r dV

4 Find Po to P4 Taylor polynomials about f x cos x at xo Taylor polynomials about f x cos x at Xo

3 Find the Maclaurin polynomials of orders n 0 1 2 and 3 for In 1 x

2 Use an appropriate local quadratic approximation to approximate tan 61

30 What is the solution set 3TT 37 TT 2 a TT 3TT 2 2 C 0 TT d 0 1 3 b 3TT 2 2

TT 9 What are the extreme values of y cos x cos x 1 4 a 75 and 75 TT TT 2 2 b c d and 1 and 1 II and II

15 What are the extremes of y sin x a 2 and 2 b C 3 and and 3 d 1 and 1 3 TT x 1 3 3

Drew s monthly net income is 2 900 What is the maximum he should use on debt payments Maximum monthly debt payments

Insects destroyed a crop at the rate of 100 2 6 M B O 125 C 88 L 100 50 tons per day where time this measured in days To the nearest ton how many tons did the insects destroy during the time interval 7 St 14

Assume that y is the solution to the initial value problem y 6y 6 sin x X 6 x 0 X 0 y 0 6 Find a Taylor polynomial approximation of degree 4 of the solution of the differential

K Fill in each blank so tha In the metric system 1 1 cm m and 1

70 Find the volume of the resulting solid if the region under the curve 1 x 3x 2 from x 0 to x 1 is rotated about a the x axis and b the y axis

Part 1 of 2 O Points 0 off 6000 seat theater has tickets for sale at 24 and 40 How many tickets should erformance to generate a total revenue of 175 000 the number of tickets for sale at 24 should be

Consider lim 8 2 818 a lim 8z 2 11 lim 00 b If we let t 8z z then we can rewrite the original limit as 4 16 t x 0

The graph of y f x solid and its tangent line at x 0 dashed is sho line is also marked Assume f x is continuous N A 10 9 8 7 6 5 4 3 2 10 9 8 7 6 5 4 13 2 f 7 8 9 40 1 16 8 9 10

Evaluate the limit lim 12xe 4 using L H pital s rule x x After applying L H pital s rule the limit becomes fill in a function lim x x Then the answer is fill in a number

Evaluate the limit using L Hospital s rule 10 11 X lim x 0 X

onvert to a logarithmic equation 16 The equivalent log Use integers or fra the equation

If Lola Harper had the following itemized deductions should she use Schedule A or the standard deduction The standard deduction for her tax situation is 12 000 Tax Deductions Donations to church and other charities Medical and dental expenses exceeding 10 percent of adjusted gross income State income tax

Write the factored form zeros of 1 4 2 and y x

Question 37 The phone company A Fee and Fee has a month monthly fee and then a certain amount of mone 130 minutes the monthly cost will be 71 5 If th be 211 5 A Find an equation in the form y mx b w y is the total monthly cost of the A Fee and Fee p Answer y

Use integration by parts to evaluate the integral 512x cos 82

Use integration by parts to evaluate the integral Cre 2x

nd from the Metric System The table shows information recorded about the location ar a Determine the altitude in miles b Determine the ground speed in miles per hour c Determine the headwind in miles per hour d Determine the temperature in degrees Fahrenheit using The altitude is about 6 09 miles Round your answer to the nearest hundredth as needed The ground speed is about 439 38 miles per hour

Differentiate the function y 2 6x 5 3 2x 9 y 0

If the partial fraction expansion of 7x 1 x 6x 5 then A R A x 1 7x 1 x 6x 5 B x 5 is

The partial fraction decomposition of where f x g x 20x 44 8x210x7 can be written in the form of f x g z 2x 1 4x 7

The length of the curve x et cos t w for 0 t 5 is

A solid is generated by rotating about the z axis the region in the zy plane bounded by the curves y 9 z 1 x 5 and y 0 The volume of this solid is

For the function find the point s on the graph at which the tangent line has slope 3 y 0 025x 5x The point s is are Simplify your answer Type an ordered pair Use a comma to separate answers as needed

Differentiate 0 y X5 dx 5 X5 5 X G X G II

3 2 1 4 3 2 1 1 2 3 4 2 3 The graph above and below is the DERIVATIVE graph of a function f f is defined on the domain 5 5 A On what interval s is the function f increasing use and U to combine more than one interval B On what interval s is the function f decreasing use and U to combine more than one interval C At what input s is the function f at a maximum separated by space or comma D At what input s is the function f at a minimum separated by space or comma 5 4 3 2 1 4

Consider the function h x 4x 36x 30 Differentiate h and use the derivative to determine each of the following All intervals on which h is increasing If there are more than one intervals separate them by a comma Use open intervals and exact values h increases on All intervals on which h is decreasing If there are more than one intervals separate them by a comma Use open intervals and exact values h decreases on The value s of x at which h has a relative maximum If there are more than one solutions separate them by a comma Use exact values h has relative maximum s at x The value s of a at which h has a relative minimum If there are more than one solutions separate them by a comma Use exact values h has relative minimum s at x

Consider the function f x 3x 6x on the interval 4 4 Find the average or mean slope of the function on this interval By the Mean Value Theorem we know there exists at least one c in the open interval 4 4 such that f c is equal to this mean slope For this problem there are two values of c that work The smaller one is and the larger one is

Find the derivative of the function f x 5 f x x 2 X 2 x 2 4 x 2 5 X

Find the derivative of the function f t 6 t 9 5 f t

Find the derivative of the function f x e4x 9

Compute the derivative of k 0 x 2 k k3 What is its domain

work 2 7 De 16 0 11 answere stion 11

work 2 7 Derivatives of 16 0 11 answered estion 5 the equation below find dy

f f x is a linear fu f x Question Help Dv

Gerry bought 8 rakes He sold them for a total of 76 85 thereby making an overall profit of 17 73 What was his average mean cost per rake

Given the following set of data 8 3 1 6 9 Please state the median

Given the following set of data 2 4 7 10 4 Please state the mode

Factor out the greatest common facto polynomial 8f 3 6f

x 4x 4x Identify any horizontal asymptotes of the function f x X t 50 H Ox 0 Oy 1 Quizzes Phoenix 2 e TMD Ok Z D IL