4) state laylors your estima te 5) Using in Taylor's Theorem, show that the error in 3) for cos (r-1)is less than. 0001.

Q: 10. Show that 2" + 42' + 8z = 0 if z = e-2=(sin 2x + cos 2x).

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Q: 10. Since (7,-1) is a point on f (x) cos z,which point will be found onf'(x) = cosx ? %3D O a (1,ח)…

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Q: 7. Prove that: (3) (a) (4) (b) sin20 cos20-1 in (-0) + cos (- 0) = cost -cote =

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Q: Show that (cos 0 + i sin 0)" = cos n0 + i sinne for n = 3 and n = 4.

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Q: sec(θ)=11/3

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Q: Q3) Ify = in[sec 8 + tan 8) find

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Q: 2) DISCUSS The Contmuyo f Sin TX %3D

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Q: Show that 2 sin 0 + sin 20 sin 0 1- cos 20 1 cos e Prove that (G) 1 T 1 tan-1 + sin V5 3. where…

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Q: If x = sec e - cos e and y = sec" 8- cos"0 (x² + 4) (* - n°(y² + 4) = n²(v² + 4) Prove or disprove…

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Q: Obtain an upper bound for the error of the approximatio cos(0.3 rad) = 1 - (0.3) / 21 + (0.3)" / 4!…

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Q: 5. Show that cos x = x has a solution in the interval [0, 1]. Hint: Show that f(x): = X cos x has a…

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Q: snip

A: Given, cosjx,coskx, ∋j≠k, k≥1 if inner product of two function f(x), g(x) on the interval [a,b]…

Q: [o,1] Find the sne exponsion of fla)=x+2 in in Sine Sinlntix), %3D 00 4-(-1)^ %3D •Sin (nTx) (c) Sin…

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Q: The integral ¹S. 01-fese csc ³0 de sin² sin ²0 de = [sec³ sec ³0 de + cos² cos²0 de dx (x²+4)² can…

A: We have to solve Integral

Q: Show that (cos 0 + i sin 0)" = cos n0+ i sinne for n = 3 and n = 4.

A: Since you have asked multiple question, as per company guidelines we will solve the first question…

Q: 12 "2 If Y= \n(Sinae), Prove y =y=- ノ

A: Here, the given function is: y=ln(sin x) So, y'=1sin x(cos x)=tanxy''=ddx(y')=ddx(tan x)=sec2x

Q: 82. Show that cos at cos bt %3D In

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Q: 3. Solve the following IBVP: Ut = Uzz + sin(37x), 00, u(0, t) = u(1, t) = 0, t> 0, u(x, 0) =…

A: Solution

Q: Prove the following equation : Cosh(3 x) = 4 cosh³(x) – 3cosh(x)

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Q: 1) Find thesexact value o niSinG/2) ban sin x Ei Joven that 4 2.

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Q: 5. Estimate to 4th place accuracy, i.e. within 0.00005 of cos(2º) using its Mac- xpansion. Justify…

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Q: 3. Prove that: tan-1z +z %3D

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Q: 4 cos z Evaluate S 16-y2 ydxdydz

A: To solve the given triple integral ∫0π∫04cosz∫016−y2ydxdydz…

Q: Evaluate the integral | : sin 20 do 3+ cos 20 using the substitution u = 3+ cos 20. sin 20 Op 3+ cos…

A: In this question, we need to evaluate the integral ∫sin 2?3+cos 2?d? using the substitution…

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: Find the length of the path over the given interval. (6(0 – sin(0)), 6(1 - cos(0)),

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Q: 3. Give upper and lower estimates (in terms of n alone) for sin nb COs na + valid for all a, b; show…

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Q: a) By using convolution theorem, show that 1 (sin 3t – 3t cos 3t). 54 1 L-1 (s² + 9)2

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Q: (a) Evaluate by parts: |x cos4xdx

A: In this question we have to find solution by using Integration by parts.

Q: By the samc way, prove that g 7 sinw.k MUIS Z N-27 cesW. +1

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Q: .If z = e-(sin x + cos y), show that a²z a2z az ax2 ду? at

A: Given - z = e^-t( sinx + cosy)

Q: Let C be the shortest path that connects a to ni and I = fe (sinhz + 1)dz. Then None of these…

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Q: 4 Giren tan A =– where 0<AS Find 2sin 2A.

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Q: 12. Write an éxpression that gives all sölutions to the equation. COS X - SIn x 3= 2.

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Q: Given: z = sin 3x cos 4y Find: z ду2 -3 cos 3x sin 4y -9 sin 3x cos 4y -12 cos 3x sin 4y -16 sin 3x…

A: Differentiate the given function partially w.r.t y keeping x as constant   ∂z∂y=sin 3x×4-sin 4y…

Q: 1. By considering (1+ expi®)", prove that "C, cos r0 = 2" cos"(0/2) cos(n /2) (ii) ►"C, sin r® = 2"…

A: First, expand the given complex function:

Q: Find the value of s in the interval (0, n/2] that makes the statement true. Round to four decimal…

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Q: Use Simpson's rule with n = 4 to approximate /" cos(2) -dr

A: Given: ∫16cosxxdx Here a=1, b=6 and n=4  h=b-an∆x=6-14∆x=54∆x=54

Q: How do you evaluate ∫ sinmx cosnx dx if m is odd? What if nis odd? What if m and n are both even?

A: If n is odd use substitution with u=sin x, du=cos xdx and convert the remaining factors of…

Q: /2 Evaluate using Wallis' Formula: sin5 x cos6 x dx

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Q: 9 If f(0) = cos 0, cos 02 cos 03 ..... cos 0n %3D Show, {tan 01 + tan 02 + tan 03 + ... + tan 0,} =…

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Q: Suppose the true relationship of Y and X, Z is given by 1. Yi = B1Xi + B2Zi + ei under classical…

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Q: Evaluate the integral. sin (6t + 17) -dt CoS 2 (6t + 17) sin (6t + 17) dt%3D cos 2 (6t + 17)

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Q: The position of a particle moving in a straight line is given by s(t) = e-*cos(5t) for > 0, where…

A: We have to find the necessary equation that must be satisfied.

Q: (6) Given that In= tan" x dx, show that, for n 2 2. %3D In- In-2 = %3D n- 1

A: I think given question is slightly wrong. According to me the required proof should be…

Q: 9 If f(0) = cos 0 c • cos 02· cos 03. ... cos On f'(0) Show, {tan 01 + tan 02 + tan 03 + ....+ tan…

A: We have fθ=cosθ1·cosθ2·cosθ3....cosθn                 ....(1) Now, we have a formula…

Q: Find the exact values of sın 20 and cos 20 for cos e on the interval 0° S 8590° sin 20= 0.7744, cos…

A: Use the identity sin2θ+cos2θ=1 to evaluate the value of sin θ. sinθ=1-cos2θ=1-372=1-949=4049=2107

Q: The solution of some second order linear DEQ is exp(-7x)[5sin(1x)+ 7cos(1x)] which can also be…

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