Wallis' formulas. 1) Prove the formula sin"-tx cos x n-1 S sin" x dx = S sin"-2x dx 2) Use that formula to prove prove Wallis' formulas: (n-1)(n-3)...(4)(2) n(n-2)...(5)(3)(1) | (n-1)(n-3)...(5)(3)(1) n(n=2)...(4)(2) ifn >1 is odd S/ ´sin"x dx = if n > 1 is even 3) Show how the substitution u = - x shows that S2 sin" x dx = S7² cos"x dx 4) Use the formula to find 2 sin'x dx and sin®x dx

Q: 1. Warmup question: What is the largest value that | sin(0)| may take for any ? What is the largest…

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Q: Prove the following identities: tan(v) + cot(v) (a) sec(v) csc(v) 1- sin(0) (b) cos(0) 1 SE cos(8)…

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Q: cos (x sin )=√₁ (x)+2 J₂ (x) cos 26+2 J₁ (x) cos 44+... sin (x sin )=2 J₁ (x) sin +2 J, (x) sin 36 3…

A: Using generating function of Bessel functions

Q: Show complete solution how you obtained rị and r2 If ri r2 then put r¡ as exponent of the 2nd term…

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Q: Suppose f is continuous, positive, decreasing, and concave up on the interval [5, 15]. Compare each…

A: 1) > left sum will be greater than right because function is decreasing 2)  < because…

Q: How be came? -1 tan (2w) tan - -1 ω -1 tan 3 82 (4/4) 3 1 + w x 1/ -

A: Step 1: Step 2: Step 3: Step 4:

Q: 1 In [cos"-1 (3x) sin (3x) +3(n – 1)I-2] 3n 1 h= sin (3r) %3D What is I, ? I.

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Q: sin x – x dx = ? X 22n (a) E(-1)". 22n+2 (b) E(-1)". (2n).(2n)! (2n +2).(2n+2)! n=1 n=1 22n+1 22n-1…

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Q: a Find the values of A and B in the identity A (2 sin x + cos x) + B (2 cos x sin x) = 7 sin x + 11…

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Q: Evaluate 13 sin(x) cos(x) dx

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Q: (5) If then eAt A = - (2 3). Select the correct answer choice. (a) I cos(t) + A sin(t) (b) I cos(2t)…

A: To determine eAt  for the given matrix A , we need to use the matrix exponential formula. For a…

Q: ſcos (x/2) cos (x/3) dx * 3/5 sin(x/6) + 3 sin(5x/6) + C None of the choices 3/5 sin(5x/6) + 3…

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Q: 21 Let z1 = 1+ 5i and z2 = 3+2i, and let z = 22 (a) Find |z| without finding z. -1 (b) Find…

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Q: If cos(0) 1 and 0 satisfies T < 0 < , find sin(0). 2 - sin(0) = %3D

A: Given: cos θ=-16 &amp; π&lt; θ&lt;3π2 To determine: sin θ

Q: How be came? -1 tan (2w) tan - -1 ω -1 tan 3 82 (4/4) 3 1 + w x 1/ -

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Q: (b) (i) Given that cos.x=0, show that the equation sin 2x cos x cos 2x can be written in the form 2…

A: As we know that sin2x=2sinxcosx  and cos2x=1-2sin2x

Q: If f(t) = cos t and f(0) what is the exact value of 4 f(0) + f(0+ 27) + f(0 + 47) ?

A: Given : f(t) = cos t and f(θ) and -1/4

Q: 2 (cos+ i sin; ) 22 = 3 (cos+ i sin ev The value of z1 = = 31 cOS evaluate: (a). Z1 • Z2 (b) 22

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Q: 13 x <0<T, find the exact value of each of the following. 5 2 Given that cos 0= (a) sin (20) (b) cos…

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Q: 1- How many roots does each of the following equations has? a- Cos x=e* b- e*= 1+ Sin x c- Inx=x² d-…

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Q: 1 c-1 83 + 4s (A) (1 - cos 2t] (B) 를[1-cos 2t (C) [1 – sin 2t]

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Q: Find at least one solution to the following equation: sin(x² – 1) 1– sin(x² – 1) = sin(x) + sin (x)…

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Q: Find 四 dx Ix=1 if y = 7x-6*

A: y=17x-6   dxndx=nxn-1

Q: (-1)"x2" Σ (2n)! 1. For all x E R, cos x = n=0 +00 (-16)"(4n+1) (2n)! c. Use the result in item 1(b)…

A: We have to prove the sum of series.

Q: Find all exact solutions on [0, 2n). (Enter your answers as a comma-separated list.) sec(x) sin(x) –…

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Q: sin x+sin x=1 and pcos" x+q cos" x+r cos x+s cos° x-1- 0 then find the value q+£+qs = ? i = sb ++E…

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Q: How be came? -1 tan (2w) tan - -1 ω -1 tan 3 82 (4/4) 3 1 + w x 1/ -

A: Step 1: Step 2: Step 3: Step 4:

Q: sin(0-a) + 3 sin 0+ sin(0 + a) cos(-a) +3 cos 0 + cos(0 + a) (i) Prove that =tan 0 for all values of…

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Q: Verify the identity. (1 - sin?(t) + 3 cos²(t))2 + 16 sin?(t) cos?(t) = 16 cos?(t) (1 - sin?(t) + 3…

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Q: Using the following definitions: sin (a) sin² 0 + cos² 0 = 1 (b)(cos) = - sin (c,d) sin(0₁ ± 02₂)…

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.