Find the Fourier series of the function: : -2 < a < -1 -1 < a < 1 03; 0. f(x): 1< x < 2 2k f (x) = 1 sin() cos( O i. = (2)f + - cos( sin( n=1 O ii. f(x) = 2k cos sin( 2 n=1 O iv. f (x) : sin() cos(- %3D n=1

Q: sin i dt 48. Let F(x) = | Show that x3 F(x) = x - x5 x7 +... 3. 3! 5. 5! 7.7! Evaluate F(1) to three…

A: Given integral is: Fx=∫0xsin ttdt Fx=x-x33·3!+x55·5!-........... We have to find F(1).

Q: 1 e function f (x) = ,x E [-27, 2nt| is continuous on: 1-cos x

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Q: What is the range of f(x) = cos¯¹(0)? A [-] 2 2 B [0, π] C [-1,1] D (-∞, ∞)

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Q: and sin x<0, find: Sin (2x) If cosx = 12

A: cos(x) = π/12  Then,  sin(x)  =  1-cos2x  =  1-π2122  =  144-π212

Q: The undefined integral of the function [x. (x - 2)] power -1 is * O sin [ exp (x-2/x) power 0.5] + c…

A: We will find the undefined  integral as following.

Q: Make the orthagonal set of functions {1, cos(x), cos(2x), ...} orthonormal on the interval [0,2pi].

A: Two distinct functions f and g are said to be orthogonal on [a,b] if &lt;f,g&gt;=0   , where &lt; ,…

Q: 35 x*-30 x*+3 If the Legendre polynomials P,(x) = then: 8 Find 1) S, x P,(x) dx 2) P's(-1) A) Lx*…

A: We will solve both these questions using basic knowledge of Legendre Polynomials.

Q: The derivative of f (#) cos(-2 a +a - a2 - 2 a +1) is O f (a) = (8 a° – 3 a? +2 a + 2) sin (-8 a + 3…

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Q: Sinx e* lim x→0 x- Sinx (b) If x = cos0,y = cosm0;m is an integer greater than unity, prove that %3!…

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Q: Solve (tan(z) - 1) (3 tan(x) +√3) o over the interval (-∞, ∞).

A: Here is the solution:

Q: Consider the 2n-periodic function f(x) = cos²(x) + sin³ (x). (i) Calculate the Fourier coefficient…

A: Here given that for 2π periodic function, f(x)=cos2(x)+sin3(x). We calculate a0,a1,a2,an(for…

Q: BIJ Compute the derivative f'cts for 5./ fcto= log (x

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Q: (a) Show that y = 3a²x - x³ is strictly increasing for a < x < a and that on this interval y…

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Q: Let h(x) = tan(2x + 7). Then h' (3) is and h'' (3) is

A: Given query is to find indicated derivative

Q: Evaluate 2х— 7 -dx J x2 — бх + 10

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Q: 1 -x2 + 6x dx = 10 - A In |-x2 + 6x - 10| + C -tan-1(x – 3) + C C -tan-1 (x + 3)+ C D tan-1(x – 3) +…

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Q: [8] Find the complex Fourier integral representation of f(x) = e2x 0 |x| < 1, |x ≥ 1.

A: The given problem is to find the complex Fourier integral representation of the given function.

Q: Classify the zeroes (according to order) and isolated singularities of (2² - 1)e¹/² cos (TZ) (z + 2)…

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Q: Find the minimum value of the function f(0) = 20 - 3 sin on the interval [0, π] O 2π None of these 2…

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Q: Use De Moivre's theorem to prove the identities (i) sin(40) = 4(sin(0) cos (0) – sin° (0) cos(0))…

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