. Let Show that, Hence show that •2T F₁(x) = 2/1/² 0 Fn(2) = eix cos ∞ N=-∞ eix cose eine de in Jn (x) in Jn (x) eine

Q: Find F as a function of x and evaluate it at x = 0, x = π/6, and x = ¹/2. X 6²c F(x) F(0) F(T) =…

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

A: Given that      f(x) = ∫0x[(t2-1)/1+cos2(t)]dt  Here we have to find at which value of x does the…

Q: Evaluate S Vx – x² dx -

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Q: Let a>0 and b be a real number. Use integration to confirm the following identities. 00 a -ах e cos…

A: Since multiple questions are asked, answering first with all sub parts. ∫0∞e-axcosbxdx=aa2+b2

Q: Let the function ƒ : R → R be given by 1- cos(x) if x + 0, f(x) := if x = 0. %3D 1 Prove that f is…

A: The solution is given as

Q: 4. Let em² cos , 2.x + b, r 0 r>0 h(x) = %3D where b is a constant. (a) Explain why h(x) is…

A: We need to solve continuity problem.

Q: A X(t) = [² 2x+ JUC) Find A-¹ by the Cayley-Hamilton Theorem X26) = (-₁ [SI-A)-¹(x (0) Find X(2) if…

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Q: Find f(x) such that f'(x) = 0. Select one: O a. f(x) = 2e² O b. f(x) = 1+ arctan(x) O c. f(x) =…

A: Value=?

Q: dx 5. Evaluate the following tanº(x) cos4(x) tan'(x) [7tan²(x) +9] + C 36 tan(x) + =tan(x) + C…

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Q: Given f (x) = |x| for x E [–n, 1] Show that 4 cos(2n – 1)x |x| = 2 E - - - (2п — 1)2 n=1

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Q: Let r(t) = cos(t) i + 4 ln(t² + t)j + 5 tan¯¹(t) k. Find 7' (t).

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Q: S-) Find the general soluhon of sin'x y"-(25inx.cos x)y'+ Ccosx+1)y = Sih? x given that y-sihx and…

A: Please check step 2 for solution

Q: u = t+1.3 -sin(u+t +5.09) with u(1) = 0.29 Let . Approximate the maximum value of ult) to 5…

A: If any function has a maximum value at a point , then at that point derivative of the function is…

Q: Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros…

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Q: What is the average of f(x)=2 cos (x) + 2 e between x=-3 and x=2 12- 10- -3 -1 00 8 6 2- 0 T 1 X 2

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Q: Find the value of (f o g)' at x = 1. Tu f(u) = cos u= g(x) = 4/x (fo g)'(1) =

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Q: 5. а) Factor the polynomial f (x) = 3xª+2x³+2x² +2x-1 into irreducible polynomials in C[r], R[7),…

A: In complex number, .

Q: cos(x) dx = dx. Use - 0o (1+x²)² o cos(x) 00 cos (x) Compute Jo 1+x²)² dx. Note that 2 (1+x2)2 the…

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Q: Using the substitution t = tan(), the integral 2 dx sin(x) – 78 cos(x) can be written as dt 39 – t-…

A: To make substitution and re write the given Integral.

Q: Which of the following finite difference scheme can be used to estimate the first derivative?

A: The finite difference scheme is an approximate method of getting the solution of  partial…

Q: Solve y (4) and z (4) applying the solution For of systems linear dipperential equation. 야 + z ty z'…

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Q: Let k1, k2 be constants and consider the ODE y" – (k, + k2)y' + k, k2y = f(x), whose auxiliary…

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Q: If y = exp(-x²) show that = -2xy and hence prove that, for n > 1, y(n+1) + 2xy(") + 2ny(n-1) = 0.…

A: Given that : y=e-x2. Therefore,  dydx=ddxe-x2=e-x2.-2x=-2xy  , as y=e-x2. Hence proved that…

Q: which of the following property is correct for J (x) d dx n-1 .a d (x" Jn (x))=x" Jn+1(x) dx .b d…

A: For Bessel function ddxxnJnx=xnJn-1x

Q: a. Let In = strate that exp (nx) sin (exp (x)) dx. By making an appropriate substitution, or…

A: Given Data: Let us consider the given data, (a) Let In=∫expnxsinexpxdx. By making an appropriate…

Q: 2. Find g'(x) for g(x) = x cos-l-V1- r²+ez³ cos z. [Simplify answer as much as possible.]

A: topic -derivative

Q: Hose ²²+x+(²-¹)y=0 dy+(x²-n²) y=0 by substitution x== 1102 at *ai 21 noite may Hence show that it…

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Q: 6. Suppose f(2) is analytic in |2| 1, and f(0) = 1, f(0) = 2, compute: %3D (1) h = fe(s+ 1)2d: (2)…

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