(§5.4, Q42) Calculate So™ f(x) dx, where sin x, x < T f(x) = -2 sin x, x > T

Q: Compute the following: e) dx (2019 + seC x tan x (b)() dr

A: a) The given integral is evaluated as follows.

Q: 0 T/2 f(x) | 1 X -1

A: Solution-

Q: E. Prove the following: 四- Iz.l 1.

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A: The Mean Value theorem states that for a continuous and differentiable function f(x) on the interval…

Q: 1. Use the Fundamental Theorem of Calculus Part II to evaluate each of the following: 1 3 a) + 8*…

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Q: Exercise 3. [On the back of this page] Determine if , is larger or smaller than 1+x 1 x + sin? x for…

A: We have to solve given problem:

Q: Find h'(x) if h(x) = x³e*sin x. O a. h'(x) = 3xe*sin x + x'e*sin x + x'e*cos x 3X, O b.h'(x) =…

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Q: Show that the p.d.f. of Z? is given by g1(x) = cosh(vAr), x > 0, wh cosh(z) = }(e² + e-=) is known…

A: Hello! As you have posted 2 different questions, we are answering the first question. In case you…

Q: Use the Fundamental Theorem of Calculus,Part 1, to find the function ƒ that satisfies the…

A: We have to use the fundamental theorem of Calculus Part-1 to find the function f that satisfies the…

Q: Find the d. c. of T from definition.

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Q: 10. a. Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the functions:…

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Q: 11) Simplify the following with both versions of the Fundamental Theorem of Calculus: e2t dt dx…

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Q: Pron a. If u = f(x, y), where r = e' cost, and y = e' sint, show that (3)³ + (3) ² - - ² [(-)* +…

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Q: Evaluate and approximate f(x) dx of the functions in Table 3. ,2 4 1/(1 + x*) V1+ x² | sin(y) e

A: NOTE: According to guideline answer of first question and first three subpart can be given, for…

Q: If S", f(x) cos(mx)dæ = } g ar cos(n²a) f(x) = Ln=1 nt +1 then m =

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Q: Chapter 4] If f(x) = dt, where g(x) = 1," (÷) V1+t3 [1 + sin(t²)] dt, find f'

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Q: Q1. Use the Fundamental Theorem Of Calculus and the Newton-Leibnitz rule to answer the following: 1.…

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Q: 3. How would you classify AG? A J G

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Q: In ΔFGH,  FH is extended through point H to point I, m∠FGH=(x−2)∘,  m∠GHI=(4x−5)∘, m∠HFG=(x+19)∘.…

A: Given that     FGH is triangle. FH is extended through point H to point I .

Q: B. Solve the following linear independent and Wronskian. 1. Are the functions y (x) = sin xand y2…

A: We have to check

Q: Use the variation of parameters to find the general solution of the following ODE. z'' + z = tan2 x

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Q: Given the function g(x) = :/ V4 + sin(31) dt, 2x3 use the Fundamental Theorem of Calculus Part 1 to…

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Q: 2 (b) S(2 + tan (0))do (c) S 2'(1 + 5')dt

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Q: 57. Use the substitution u = x/3 to prove dx 1942=tan 1+0 www C 9+x² 3 3

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Q: 3. Use the Intermediate Value Theorem to show that the following equation has a solution. sec(x) =…

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Q: d 5. Prove (arccot(x)) dx -1 Be sure to provide a written justification for your work. 1+ x?

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Q: Prove the following: d -1 arccos(x) dx V1- x2

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Q: Find the least positive root of f(x)=x cosx-1 as shown in Figure Q1(c). (c) -4 -6 -8 +-10 Figure…

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Q: he coefficient ao of Fou +2 t. く?

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Q: Find the greatest value of F (x)= | (6 . cos t - 2 sin t) dt 5 7/3 in the interval [5/3,7 t/ 4|.

A: Fro the given problem: Fx=∫5π/3x6cost-2sintdt Now solve the above definite integral,…

Q: Use the TRAPEZOIDAL with 3 level Romberg (k = 3) to evaluate: e* sin x 1+ x²

A: Answer is mentioned below

Q: J sec° (10t) tan“ (10r) dt 4 10.

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Q: 1 Q4\Given the function f (x) : Find S f (x)dx 1+sin x'

A: ∫11+sin(x)dxRewrite using trignometric identities:=∫sec2(x/2)(tan(x/2)+1)2dxSubstitute…

Q: Given f(2) = . t2 – 1 dt 1+ cos?(t) At what value of x does the local max of f(x) occur? x =

A: Given the function

Q: Find fogo h. f(x) = 3x – 4, g(x) = sin(x), h(x) = x²

A: Answer is mentioned below

Q: Section 5.5 p. 593 # 296 In the following exercises, use a change of variables to evaluate the…

A: We have to find

Q: The linear approximation to fix) = E at x = 8 is given by O a. 2 - x Ob. 2 Od. 12

A: Given: f(x)= x3 Linear approximation of a function fx is given by the formula  y=fa+f'ax-a

Q: If f(x,y,z)=In(x²y+sin?(x+y))+111x112y2z113, then at (1,1,1) is equal to əx²əyəz

A: We have to find derivative

Q: The function f(x) sin x + cos x is an even function. True False

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Q: The equation implicitly defines z as a function of t. Find dz dt +² 22 - sin (5 z) = -8

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Q: Given +2 – 25 dt 1+ cos2(t) f(x) : At what value of x does the local max of f(x) occur? Preview

A: Consider the given function.

Q: Chapter 12, Section 12.1, Question 003 Find the domain of r(t) and the value of r(to). r(t) = cos…

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Q: Find the absolute minimum and absolute maximum values of f on the given interval. f(t) = 4 cos(t) +…

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Q: B) f(x) = x+3 (-6, 6<x<1 Is f cont. at x-6?

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Q: given the function f(x)=(ax+b)cosx, where the function is increasing at x=pie/2

A: We need to check if the function is increasing at x.

Q: Use the TRAPEZOIDAL with 3 level Romberg (k = 3) to evaluate: e* sin x , 1+x²

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