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: - 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: -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: 3 п (3 2 sin (x-2п) cos ( -x ) + tan (п -x) tan 3 п 2 +x

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

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: 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: cos(x) sin (2x) lim x X sin(x) – 1

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Q: prove the following identities: cos² (y) - sin² (y) 1 - tan² (y) = cos² (y).

A: according to bartleby guide line we do only first part of multiple questions prove…

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: 1-sin x x1 + cos2x 2 5) lim 6) lim sin x-cos x TC 4

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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: If x sinx < 1 2 - 2 cos x hold for all values of x close to zero. Find limx¬0 xsinx ? 2-2cosx

A: 1-x26&lt;xsinx2-2cosx&lt;1 holds for all values of x close to zero. Now, limx→01-x26=1-0=1 &amp;…

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: 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: 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: The value of a and b so that X(1 + a cos x)- b sin x lim =1 are .3 to 3 3 5 (b) 2 2 (a) 3 5 (c) 2 2…

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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: 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

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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