(b) Find the values of a and b so that the function f(x) = x² + ax + b has a local maximum at the point (8,1).

Q: Consider the contour represented in the following figure. The points marked on the figure are А(5,…

A:

Q: A. Evaluate the following integrals. 1. S(Vcos x + sin x)´dx 2. S cos³ 3x dx 3. S tan5 2x dx

A: To evaluate the following integrals.1 ∫cos x+sin x2 dx2 ∫cos33x dx3 ∫tan52x dx

Q: where did you get 9.9999

A:

Q: What are intervals of concavity of the function f(x) = 2x - 6x² – 3 ? Concave upward on (1, o) and…

A:

Q: 2. All straight lines with slope and y-intercept equal. У (x + 1) — у %3D0 ans.

A: It can be solved as follows

Q: Solve the problem and give a detailed solution. Find the 3rd derivative of y = sin(ex)

A: y = sin(ex) Differentiate w.r.t.xy'=ddx( sin(ex) )y'=cos(x)ddx(ex )y'=cosexexDifferentiate again…

Q: 8x2 – x + 8 x(x² + 4) G) + 1 2 In x + 6 In (x² + 4) – ; Arctan () + 4 In x + 3 In (x² + 4) – ;…

A: Topic:- application of integration

Q: (-1)" „2n for all x E R. (2n)! Consider the series expansion of the cosine function cos(x) = > n=0…

A: nth degree Maclaurin polynomial for f(x) :       f(x) =∑ i=0n fi(0)i!xi   =…

Q: Set up iterated integrals for both orders of integration. Then evaluate the double integral using…

A:

Q: What are the first three non-zero terms in the Maclaurin Series of f(x) = e* sin(x)? a. x+++-- + ..…

A:

Q: Find an equation of the ellipse with minor axis length 6, and vertices (3, 1) and (3,9).

A:

Q: Evaluate the following. Give an exact answer, not a decimal a a) csc 2 b) sec ä

A: Topic:- trigonometry ratios

Q: dr Vr – 9 3

A: We can find the integration as below.

Q: (c) cos 27 (d) tan

A: Cos(π/4)= 1/√2= 0.707106781

Q: Evaluate the indefinite integral: tan(0) cos(0) c

A: Given: ∫tan2θcosθdθ

Q: Let f(æ) = (4sin æ + 2 cos a)arctan e f' (2) =

A:

Q: The market research department of a company recommended to management that the company manufacture…

A:

Q: can you write it on paper, I don't understand it like that

A: We have the solution as follows:

Q: 3 csc x cot x dx 3

A: Given query is to find the integral.

Q: 3.

A:

Q: dx 1-Cos r

A: The Given integral is 1/(1-cosx).

Q: 3. dx

A: Integral CalculusExtension of power formula

Q: The

A:

Q: Kindly recheck your answer thank you . What is the area of the region bounded by the graphs of y?…

A:

Q: On step 5, where did the 8 come from in x-3+8?  This is where I'm stuck

A: ∫au+bn du =1aau+bn+1n+1+C ∫11-u2 du =sin-1(u)+C

Q: dy Solve (x2 + 2y) 교 = xy; y(-1) = 1 dr

A:

Q: Select the correct answer. 12 , 30 lim Sn? what is the value of noo If O A. 24 O B. 50 OC. 84 OD. 75

A:

Q: Which of the following statements is true about the function f whose derivative is f'(x) = (x –…

A:

Q: Directions: Analyze and solve the following items. Show your complete solution and box your final…

A:

Q: dy Solve of y = e2-3+18 In(e2²-30+18 da A. y' e2z²-32+18 (8x3 – 18z² + 85x – 57) B. y' e2a2-3a+18…

A:

Q: There are two lines through the point (−1, 3) that are tangent to the curve x^2 + 4y^2 − 4x − 8y + 3…

A:

Q: sin* x cos? x dx

A:

Q: 10% -10 -5 5 10 -5 -10 Find the direction angle of vector v to the nearest tenth of a degree.

A: The graph is To evaluate: The direction angle of the vector.

Q: Question 2 Construction Problem A farmer has 180 ft. of fencing to be used in the construction of…

A:

Q: A quadratic polynomial y = 4x² + 7x – 3 has roots p and q. Find a quadratic g(x) = x2 + ax + B with…

A:

Q: how did you get infinity

A: we need to know that limx→∞(x)=∞ and limx→∞x2=∞and∞=∞

Q: 4 x 1 dx Vx+9 6+,

A: To evaluate: I=∫4xx2+9dx

Q: Your interpretation and answer are incorrect.  My question had fractions but you interpreted them as…

A:

Q: ) (y nx) ny dx + dy

A:

Q: 1 Verify that tan?(csc-1(x)) = x2 – 1

A:

Q: 3. If 100x units of a particular commodity are demanded when p dollars is the price per unit, x² +p²…

A:

Q: 2. The Auxiliary Equation : (4D* – 4D' – 23D² +12D+36)y = 0

A: Given: 4D4-4D3-23D2+12D+36y=0 So, 4m4-4m3-23m2+12m+36=0

Q: 8., (x + y) dA, where R is the region that lies to the left of the y-axis between the circles x? +…

A: As you have asked to answer question 8, we will answer question 8.Question 8.The given integral…

Q: Find the derivative of the function. 3 ew r = 8w dr dw II

A: Solving the problem by finding the value of the derivative.

Q: x²+2x²y=2xy+2xy²–3y The expression is equal to x+y

A:

Q: dx S. 2x - 1 e

A:

Q: SOLVE THE FOLLOWING HOMOGENOUS LINEAR DIFFERENTIAL EQUATION 1. (D^3 – 3D^2 – D + 3)y = 0

A: The given differential equation is: D3-3D2-D+3y=0 So, the auxiliary equation is: m3-3m2-m+3=0

Q: olve (x² + 2y²) = xy ; y(1) = 2 da

A:

Q: Checking using Second Derivative Test

A: From the secon derivative test, if the value of second derivative at the critical point turns out to…

Q: - dx. 3. Evaluate J9x -16 C) 271n|9x° +16 +C D) In px" +16 +C A) 27In|9x° -16 +C B) Inpx° -16| +C 27…

A: