The best approximation of f (x) = cos(3 + x) by a %3D Fourier polynomial of degree 1 is 1) F(x) = cos(3 + x) 2) F(x) = cos x + sin 3) F(x) = cos 3 cos x – sin 3 sin x 4) F(x) = 3 cos x. 5) F(x) = sin 3 sin x.

Q: f= x? + क) | + ला (i) of =? (üi, af मु] liv) of

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Q: Evaluate / 4 x cos(x)dx Ox sin(x) – 4 cos(x) + c 04 sin(x) + 4 x cos(x) + c 04 (x sin(x) + cos(x)) +…

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Q: 26) If y=sin(-0).find dy d0

A: Given.

Q: 4) Consider the function defined by 10) = /3 (sin (5 + *)) (증+0)) +4 V3 sin (+t) + 4+ V/3 (cos G…

A: we have to show that f(t) is a constant

Q: The trigonometric substitution x - 2 = 3 sec could be useful in integrating a function (i.e., an…

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Q: S Q16) L−¹ {(8 − 1)² + 4) (A) et [cost + sin t] (D) et [cos 2t+sin 2t] (B) et [cos 2t + sin 2t] (E)…

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Q: √4x+4-√√5x+1 x#3 Q18) if f(x)= x-3 k x=3 A) 15) 1 C)O by Q19) Use local linear approximation in ind…

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Q: 921) Which of the following is an odd function A) cos xsin x 11 sec.x C). DUNK DOOV

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Q: The best approximation of f(x) = cos(8 + x) by a Fourier polynomial of degree 1 is

A: The Fourier Polynomial of degree n is Fn(x)=a0 + ∑k=1nakcos(kx) +∑k=1nbksin(kx). Then, the Fourier…

Q: O t-sin(t)

A: the answer is t-sin(t)  provided the solution below with steps in step2

Q: Determine if the setsin² {sin²x, 1-cos(2x)} is linearly dependent or linearly independent on I =…

A: Let B={sin2x,1-cos(2x)}.

Q: 3. Find the derivatives: 3x3-4 a) f (x) = b) y = (x2 + 6x + 2) (+ Vx5 + 3) DO NOT SIMPLIFY 2x²+3 c)…

A: a) Use quotient rule of derivative and find the derivatives of above function.

Q: sin3x d) lim x→0 + lim cos x + lim 2x² x→2 x-3

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Q: 1. how that { cos(Inx), sin(Inx)} is a fundamental solutions set for x²y" + xy' + y = 0 on the…

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Q: a) _*? (1-x²)Z x+3 b) S- x2+2x+5 c) Find the value of sin(tan-1- sec-d) dx d) S x² Vx2+1 e) S Vx2+2x…

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Q: 2. The suitable Trignometric substitution that solves fx(x-2) dx is (x-1)=sin 0 x-1)3sec0 (x-1)=tan…

A: We can find the answer as below.

Q: Evaluate f dx V4 √4x²

A: This we directly computed by the rule of integration that is there is no any dificulty to find the…

Q: Calculate facos xdx . (a) rsinr – casz+c (b) Icosz+sin x+c (c) zcost-sin x+c (d) Isinz+cOSI+C (e)…

A: Formula for integral by parts :        ∫u(x).v(x) dx=ux∫vxdx - u'x∫∫vxdxdx+…

Q: 6) Use Linear Property to find ( 1- 3 x4)' A) (1- 3 x4) %3D B) – 4x3 C) - 2 D) - 12 x3 7) Use…

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Q: 2) Given: f(x) = (x-1) (x+ 1) was transformed to (x) = (x- 1)(x+ 1)-1. How many roots would the…

A: f(x)=(x-1)2(x+1)2 was transformed to f(x)=(x-1)2(x+1)2-1.

Q: 1. dy = %3D COSX cotytanx Cosy dr

A: Given- dy=1cotytanx-cosxcosydx To solve the given differential equation. Here we will arrange the…

Q: (1 point) Approximate cos(4.6) using a quadratic approximat First note that cos(4.6) cos(3/2). Let…

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Q: Determine f(x) so that cos(In x) f(x) dx = sin(In²x) + C

A: Option B

Q: Q16) Find the value for a,b. it f(x)= ax +4x²+bx has stationary point at x1, and inflection point at…

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Q: Example Let f(x) = sin(x). Approximate f() by the Hermite interpo- lating polynomial of degree at…

A: Given the function fx=sinπx To find the value of f14 by Hermite interpolating polynomial when x0=0,…

Q: The function f(x) = sin(kx) contains the point A(, -1). The function is: Oa) f(x) = sin(-x) Ob)…

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Q: 1+sin-1t Find A' (t) if A(t) 1-cos-1t

A: Given: At=1+sin-1 t1-cos-1 t To Find:  A't=?

Q: 2T d) f(x)=5 sin (x+1)+2 e) f(x) = -2 cos 2(x+ 1) + 1_ 17. Find the rule of the sinusoi

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Q: Graph and find the Fourier coefficients of the following functions f(x): - 1/2 < x < Tt/2 T/2 < x <…

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Q: Six)ax = [glu) du 1f flx): 3x-1 Solw) au ? Consider what is sec (3*) ·

A: we have to integrate