6. Suppose that f(x) = x" + an-1r*-1+ ...+ ao E Z[x]. Ifris rational and x –r divides f(x), prove that r is an integer. %3D

Q: 10) Suppose that f is continuous and that f(z) dz = 0 and f(z) dz = 5. Find - 6f(x) dx . -3 -3 A) 30…

A: ∫-33f(z) dz = 0  ,    ∫-35 f(z) dz   = 5find -∫356f(x) dx∫abf(x) dx    = ∫acf(x) dx   +∫cb f(x)…

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Q: 7. Find the area between f(x)=-x² + 4x and g(x) = x² - 6x +5 over the interval 0≤x≤1 Ei..

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Q: 10 Suppose that " fx) dx and Ax) dx = -5, and "g(x) dx = -1 and g(x) dx = 3. Compute the given…

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Q: Suppose f(x) is positive, continuous, and f'(x) < 0 for all z in [ – 8, 4], and / f(x)dx = 76 and…

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Q: 5. Write a 5th degree Taylor polynomial for f(x) = cos(2x) centered at x = T/4. %3D

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Q: Expand the following rational function using partial fractions. Do not integrate. 1 1? – 1

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Q: 2. Expand the function f(x) = tan-1 x up to the first two non-zero terms in the Taylor's polyno-…

A: Solution is given below:

Q: 1) Consider the function f(x) = In(x + 5) + x + 5 Verify that the function F(x) = x In(x + 5) is an…

A: Explanation of the answer is as follows

Q: 8 4 8 Suppose that f(x) dx = 7 and f(x) dx = -6, and g(x) dx = -1 and g(x) dx = 4. Compute the given…

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: 2. (a) Show that when x > 1, In(x) (This should be very short.) (b) Use your knowledge of integrals…

A: We have to show below given expression

Q: NUMMTD FE Evaluate the integral of f(x)= 400x* – 900x* +675x –200x² + 25x +0.2 between the limits…

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Q: 4. Use Taylor's Inequality to estimate the accuracy of the 5th degree Taylor polynomial…

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Q: Determine the nth Taylor polynomial of f(x) = 1/x at x = 1.

A: We know that the Taylor series expansion of a function f(x) is given as: ∑n=0∞fnan!x-an where fna is…

Q: Show that for every 0 < p < 1 the integral 1 1 sin – dx xP is both improper and convergent.

A: Answer

Q: 1. Find the maximum of the function: f (x) = 4sinx (1+ cosx ) a. Using Golden Section Search with…

A: As per bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: 3. For Z = x²secy,prove that Zxy is equal toZyx

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Q: 12.)Express lim E(3(x;,)² – 5x, + 2)Ax as a definite integral on the interval [0,1]. i=1

A: The given expression is: limn→∞ ∑i=1n 3xi2-5xi+2∆x    on interval [0, 1]   The definite integral  on…

Q: хах 11. The integral f 4-х2 is equal to 1 A. In | | + C C.-글m14- x리 + C 4 x+2 2+x B. In |4 – x2|+C…

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Q: (3) Consider the function defined as : R -> R>0 if laT 1 2 p(x) 0 if a> np(nx), and let Kn(x) be the…

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Q: Find the degree n=4 Taylor polynomial for f(x) = ln (x + 1) at c=1.

A: The degree n=4 Taylor polynomial for f(x) at c is given by f(x) = f(c) + f(1)(c)1!(x-c) +…

Q: To prove that 2 dx 2 In V1 + (In x)² + In x| + C X/1+ (In x)² we use the substitutions

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Q: 3.12 Еxpress lim n00 n k3D cos 1+ as an integral. (Be sure to include the lower and upper limits|of…

A: Given: limn→∞ 2n∑k=1ncos1+2kn To convert this into the integral , use the following method

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Q: Let f(x) = Q[x] be a irr of prime degree p. If fr non-real roots then th

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Q: 4. Use Taylor's Inequality to estimate the accuracy of the 5th degree Taylor polynomial…

A: Taylor's inequality:  Let f be a function which has Taylor series expansion centered at x=a. The…

Q: | 45. Apply integration to the expansion 00 =E(-1)"x" = 1- x+x – x +.. 1+x n=0 to prove that for -1…

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Q: 1. Evaluate the definite integral S ,2 C (9x² + 5)dx by the limit definition.

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Q: 12. Find the general solution using Reduction of Order: a) y" = In x

A: you have asked multiple questions in a single request we would be answering only the first question…

Q: 9. Evaluate the indefinite integral x'V4-x² dx . 3 Hint: Let u = 4 – x² and write x' = xx?.

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Q: Find the residue at z = 0 of the function 1 / (z + z^2)

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Q: Q4: Discuss the continuity of : 1 for x2

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Q: For f(x) = √ √2-4 4- ™ Of is not continuous at x = 4 Of is continuous at a Of is continuous at a 5…

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Q: 2 Evaluate the improper integral 4x e dx, if exists. 8.

A: Given that,           ⇒           ∫-∞2e4x dx   ,   if exist             ⇒         find the…

Q: LET F(X)=1/X.USE CENTRAL- DIFFERENCE FORMULA FOR F '(X) OF ORDER O(H4 ) WITH STEP SIZE H = 0.1 TO…

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Q: 19. f(x. y) In(1 - x - y) %3D

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Q: – 30 - Evaluate the integral: -d.x x2 Vx2 + 16

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Q: (4.4) For #27-28, find the value of c guaranteed by the Mean Value Theorem for Integrals. 27. f (x)=…

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Q: of of and Find dy for the following function. f(x,y) 3 е 4xу In (6у) of of II

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Q: 2. Prove that g(x) = sinh x + x – 1 has a zero in [0, ln 2].

A: To prove that gx=sinh x+x-1 has a zero in 0, ln 2.

Q: 19. Consider the integral f√x²+25 dx. 9x² a. In/√x² + 25 +x/- - b. x+ In/√x² + 25/+ √x²+25 9x √x²+25…

A: Solve the integral  √(x2+25)/9x2

Q: Determine the nth Taylor polynomial for f(x) = e^x at x = 0.

A: To Determine: nth taylor polynomial for fx=ex at x=0

Q: 4: Find the indefinite integral of f(u) = -1-3√ =

A: