Suppose n is an integer. So Show that for n+0, ſ x cos(nx)dx = { п n is even (a) 2 п is odd n2

Q: (In n)" c) E-1 2n+3 n! cos NT b) Σο n=1 n%3D1 n3+n+2

A: Consider the given series: Here the objective is to check whether the given series is convergent or…

Q: If y= In(4 tan (4x) ), then y' tan(4x) = Select one: 04/(1+x² ) O None O 4/(1 + 16 x² ) 01/(1+ x² )…

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Q: 3 Find the exact values of s in the interval [0,2x) that satisfy the given condition cos 2s = л 11т…

A: Topic : trigonometry

Q: Suppose m and n are constants and m #n- Evaluate * sin(mx) cos(nx) dx cos(m+n)x] + C 1 −cos(m−n)x+·…

A: Indefinite Integration

Q: Q- het m = 10-81 +3. compute the Suron E Sin (mntt) cos (m +2) (m+1)"+ COS n+1 n=1

A: The sequence of partial sums is very important in evaluating the sum of an infinite series. The…

Q: Suppose m and n are constants and m #n- Evaluate [ sin(mx) cos(nx) dx -cos (m + n)x] + C 1…

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Q: in Let z = 0.5 +",., Find e 6z 3 C) e3 F) e-0.5 (cos 2 + isin2) A) -e 20 B) e-5* (cos 20 + isin20)…

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Q: To show that rπ/2 sin" x cos" x dx: (m - 1) (m- 3) ... × (n – 1) (n - 3)... (m + n) (m + n - 2) (m +…

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Q: Find all values of x between 0 and 2pie that satisfy the quation.   cos x = -1/2

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Q: Which of the following is equivalent to the definite integral 7/2 | (cos(72) + 7) dæ? 1 [,sin(7m/2)…

A: Definite integration

Q: Evaluate (6+3 cos x) dx using Simpson's 1/3 Rule (n=4). O 12.114624 O 12.42518 O 12.386215 O…

A: Simpson's 1/3 Rule n=4: ∫abf(x) dx≈h3f(x0)+4fx1+2fx2+4fx3+fx4 Where                  h=∆x=b-an

Q: "ind no E N such that for all n > no sin(n + n² cos(n²)) n3 – 5n4 – 20 -

A: Find n0

Q: Suppose m and n are constants and m # n Evaluate O 1 1 -cos(m-n)x - - -cos(m+n)x] + C m-n m+n O 1 1…

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Q: 11) (3ysos(3a By cos(3

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Q: Suppose m and n are constants and m #n. Evaluatesin (mx) cos(nx) dx' cos(m− n)x- = cos(m+n)x] + C 1…

A: Solution is here

Q: Suppose m and n are constants and 1 n-m 1 m-n m-n m‡n. 1 -cos(m− n)x- cos(m+n)x] + C m+n 1 -cos(m−…

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Q: Suppose m and n are constants and m #n. Evaluate sin(mx) cos(nx) dx 1 Ⓒ[con(-)x-cos(m + n)x] + C B −…

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Q: Suppose m and n are constants and m‡n. Evaluate [sin(mx) sin (mx) cos(nx) dx 1 _____cos (mn)x -…

A: We have to solve integration

Q: (-1)"n" sin" () Σ n 2n n=1

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Q: Use symmetry to evaluate the followingintegrals.

A: We have to find definite  integral using symmetry.

Q: Cos 30° Sn 60° o S.n 60° Cos?0° (os 60° S.n šo° %3.

A: As per our guidelines we are supposed ro answer only 3 parts, those are given in the steps below.

Q: The approximation of * (Cos(x))²dx by Composite Simpson's Rule with n = 4 is 0.3688 0.3081 0.6427…

A: ∫0π4cosx2 dx Here, fx=cosx2,  a=0,  b=π4  &  n=4. Now, ∆x=b-an=π4-04=π16 Now,…

Q: 28- For What Values of a anel k is a X <-1 ー<くく -2 Cx) = ax-b 3 Continuons at every X ?

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Q: 2 72 Given n is a positive integer, (V3 + j)" + (V3 - j)" is 2n+1 sin O () 2" cos 2" sin (") 2n+1…

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Q: Suppose m and n are constants and mn. Evaluate sin(mx) cos(nx) dx. 1 A cos(m− n)x - cos(m+n)x] + C…

A: The objective is to find the correct option.

Q: Suppose m and n are constants and m‡ n.- Evaluate [sin(mx) cos(nx) dx 1 1 -cos(m-n)x. cos(m+n)x] +C…

A: To find the value of given integral.

Q: *(+²–1) cos[cosh (In r")]dr 4.

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Q: 2.Expand the following in powers of x i)√(1 + sinx) ii)e cosx iii) cos x²+

A: Given data:- (i); 1+sinx (ii); excosx (iii); cos-1x2-1x2+1

Q: Show that in (5.2) the average values of sin mr sin nx and of cos mI cOs na, m+ n, are zero (over a…

A: Given problem is :

Q: 3x)=てメ+cosス そし-て)- -4-cosいて) そしね)、ずした) ):-Smいて)=20348 Kntl = Kn - ぐし) 0.9651+2.0 348 32 Satisfied…

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Q: 2. If 90° < 0 < 180° and cos 0 =-, find sin. %3D 11/3 11/3 3 ) - 3V11 11 O 3/11 11

A: We know that the trigonometric identities :  cos x = 1 - 2 sin2 (x/2)

Q: Prove that Σ n=1 sin ne n - 6.² < sin x X - dx = 1.8519... for any positive integer m and any 0 in…

A: In this question we have to Prove the following given statement. ∑n=1m sin nθn&lt;∫0π…

Q: Which of the following is true? A Jcos(3x)cos(4x)ax = [ cos(x) + cos(7x), 2 ® Jsin(3x)sin(4x)dx = […

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Q: Let m be the number of solutions of sin (2x) + cos (2x) + cos x + 1 = 0 in 0<x< x< 1/1/2 and 7 7π n…

A: The roots of the equation: f(x)=0 are the values of x, where the graph of the function: y=f(x)…

Q: 1. For non-negative integers n, let k +1 k +2 Σsin n +2 n sin k = 0 n +2 f(n) = Lsin-( k +1, k = 0 n…

A: Given f(n)=∑k=0nsink+1n+2πsink+2n+2π∑k=0nsin2k+1n+2π

Q: Given x[n] = x1[n] + x2[n] where, Ttn x1 [n] = 9 cos and x2[n] = 8 sin 4 8

A: Given: xn=x1n+x2n x1n=9cosnπ4 x2n=8sinnπ8 To do: Graph x1n using Scilab.

Q: 33. If z = [i(cos 0 + isin 0)]" then arg(2) -2n0 + n A n0 + n 2n0 D 2n0 – n

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Q: The sum of the series 1 + 2" + ... is n! ... 1! 3! A In 2 B e' cos 2 D sin 2 E nonexistent

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Q: • 8 If In = 7/2 e*cos" x dx, where n 2 2, prove that: %3D (a) In = 1-n[" /2 e-* sin x. cos"-1 x dx…

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Q: D n In (1+ n=1 n16 arctan E 5" In (1+ > sin n=1 2n+1 n=1 F

A: We have to choose the convergent series according to the given options

Q: Fand ar a of functrons COSX n

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Q: -) {in(6n) 2 n=2 =) an = In(6n³ – 4) – ) {cos(nt)}0 n=0

A: e) an=ln6n3-4-ln3n3+5n2-7n+8 determine if the series is convergent or divergent? if convergent find…

Q: Suppose m and n are constants and m #n. Evaluate I sin O 1 1 -cos(m-n)x- - cos(m+n)x+ C n-m m+n 1 1…

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Q: Consider the function f(t) = 12 cos(40t), where the coefficient of t is in rad/s, and tis in…

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Q: 40. Show that cos(30) = 4 cos e - 3 cos e for all 0. [Hint: cos(30) = cos(20 + 0).]

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Q: Q2) 1- Find O for: y= cos (x) + cos(x)

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Q: 3. Prove there is at least one x E R such that e* 2 cos x +1

A: We have to show there exist x€R such that e^x=2cosx+1...... (I)  We plot the graph of both function…

Q: Given f (x) = |x| for x € [-,1 Show that cos(2n – 1)x (2n – 1)2 4 |x\ = ; 2 n=1

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