a) Show that exp(z) in the range 0

Q: 15.4 Associated Legendre Equation Table 15.3 Associated Legendre Functions P(x) = -(1-x²) 1/2 = -…

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Q: Evaluate (x2 + 1) cosx dx O (x2 + 1) sin x + 2x cos x – 2 sin x + C - (x2 + 1) sin x – 2x cos x + 2…

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Q: - 1 X If lim ([sin ¹x] + [2²sin ¹' (2x)] + [3³ sin-¹ (30)] x →0 X X + [x²³sin-¹ (x2x)]) + ... +…

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Q: Evaluate f{ [sec (x) + csc (x)] + sin ()} dx : (2)]? + sin (팔프)}dz O a. tan (x) In |csc (2æ) + cot…

A: To solve the following integral

Q: (a) [(0.6e15 + 4t 3t² +03-10-01 at 4t4-3t3 + 0.3 _10t 1.5 -0.1 2t3 (b) Evaluate…

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Q: -1 3. Show that sin-¹x = tan X √1-x² if |x| < 1.

A: Introduction: When there are trigonometric functions present in an expression or equation,…

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: tan (3r) dr = a tan(3x) – In(v1 + 9x²) +C 3 a tan (3x) + In(v1+9r²) 3. e tan '(3x) In(v1 - 9x² +C a…

A: We know that, from basic integral formula ∫tan-1x=xtan-1x-12log1+x2+C          ⋯⋯1 We have, the…

Q: 3i +2V2 - 5n -4i +6(1 +a T/4 [(3sec2 t)i - (5 + sin t)j - (6sec t tan t)k)]dt Find 0. 2 2-57T-4 3i +…

A: ∫sex2xdx =tanx+c∫(constant)dx=x+c∫sint dt =-cost +c∫sect tant dt =sect+c tanπ4=1cosπ4=12secπ4=2

Q: + tan dy 37 Ify = tan -1 -1 1 2 x +5x+7 1 2 1 2 1 2 x² + x + 1 +... to n term.

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Q: Let f(x)=2x-3,g(x)-5x, and h(x)=x2 what is the sinpliest fornm of h(x)*g(f(x))

A: Explanation of the solution is given below...

Q: T/3 3 sin (3t) -dt. 5 - cos (3t) Evaluate the integral

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Q: Let f"(x) = x'/A cos(x), /(0) = 2, and f(1) = 2. Is it true or false that 7=-73+ cos(x) + 28…

A: The answer of above solution is option A. i.e true.

Q: The Fourier Cosine transform of the function f(X) = {1, |x| a} a A 1/(/2n)*(cos(as)/s) B…

A: Given functionfx=1,x&lt;a0,x&lt;aFourier cosine transform of f(x) is given byFcfx2=2π ∫0∞ f(x)…

Q: 2 cos(5x) – 5 x² – 2 lim sin(3x) – x² – 3x - - (Write your answer in the given box)

A: We will use L'Hopital rule

Q: 7)Use Taylor theorem to estimate cos(0.23) with Jerror|< 10-2

A: Here we are to estimate cosx at x=0.23=23100 with error≤10-2,using Taylor theorem i.e, using Taylor…

Q: Show that sin (2n + 1)z 2n +1 { 7/4 */4 0<まく

A: We will use complex analysis to solve the given infinite sum.

Q: If g(x) = Cos x – Sin x a) Find g() and g (#) 8 b) Show that g ( - + x) = g(n – x) .2

A: sin(π2+x)=cosx cos(π2+x)=-sinx sin(π-x)=sinx cos(π-x)=-cosx

Q: Evaluate / 11 x cos(x)dx O11 sin(x) + 11 x cos(x) + c Oc – 11 (x sin(x) + cos(x)) Ox sin(x) – 11…

A: Topic- Integration

Q: Find sin(8) O√3 -|~ 2 √2 2 이틀 2 TT 5T/6 7m/6 2/3 4/3 TT/2 3T/2 ○ TT/3 5/3 _TT/6 /11/6 0

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Q: 12 1 dx 1+ x2 5e* 2.) / sec(a) tan(a) e* sec r dx 3.) /; 15x4 d.x 3

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Q: (5е? + 9* — 8 sin x)dx - 8 sin æ) de O 5e* + x° – 8 cosx + c x° - 8 cos x + c О Бе + x —— 8 sin x +…

A: Solving the problem by doing the integration.

Q: Sæ³ cos(x*) dæ =

A: We solve it by u part method , ∫x3cosx4dx Let u = x4 Differentiate both side , we get   du = 4x3dx…

Q: V1+ cos x + v1- cos x X =-+-,0<x<. 4 2 an 1+ cos x - V1- cos x - cOS X VI

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Q: 2x 2)/3x* 2) [3x* - 9x² +1 V9-x² dx .2 3) [ sin xcosx dx x cos.x 4) S sin² xcos 4) sin x cos x dx

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Q: Evaluate 2х— 7 -dx J x2 — бх + 10

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Q: (x²–1)dx S (x++3x² +1)[tan-1 x2-1 aluation of is

A: Given integral is I=∫x2-1x4+3x2+1tan-1x2+1xdx To evaluate I Now, dividing the numerator and…

Q: EXAMPLE 6 (a) Show that sin-1 (sin (4)) = - (b) Show that sin-" (sin ())+ + *. (b) Show that sin¬l…

A: a)

Q: (1) Use the definition to prove that if xn → 2 then (2xn + 1) / xn → 5/2.

A: As per our company guideline we are supposed to answer only first three  qs, kindly post remaining…

Q: z(r) = cos'(r)/1+r* ? cos (r) ( r Vi+r (1+r² 4 tan(r) cos'(-\/i + r*{ 4 cot(r) 1+r I tan(r) (1+r²

A: The given function is zr=cos4r1+r2.

Q: Q6) (a) Prove that Fourier cosine transform of f(x) = cos(x), 1 sin 3(p-1), sin 3(p+1) p-1 p+1 +…

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Q: QI: Choose the correct answer 1) f(3e*r - 6 sin(3x) + 10cse (2x)) dx = A)e - 2 cos(3x) + 5tan(2r) +C…

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Q: Use Simpsons 1/3 rule to find sinx

A: Please refer to the image below