1. (a) Find L{e(cos 4t – 2 sin 4t)} (b) Find L {t sin? t}. [ Recall sin? A = -24 (c) Find L-{74 4o+5 } se-3s

Q: (-9)" (2n)! (a)e³ (b) cos 3 V3 (d) sin 3 (e) None (c) cos 2

A: The given series is ∑n=0∞(-9)n(2n)!

Q: 10 - cln(2n) e cos (e") dx 0. a) О sin (1) b) O e2m - 1 c) O 1 d) O e27 e) sin (1)

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Q: 9T Find the exact value of sin( ) 4 - /3. O 1 1/2

A: We can make it easier for you.

Q: 1. Evaluate L(sin)) L(e-t cos 4t) 2. Is L(t? cos 4t) = L(t²)L(cos 4t)? c. %3D

A: 1c We have to evaluate Le−tcos4t. Apply Laplace transform rule: If Lft=Fs then Leatft=Fs−a. Here,…

Q: -2 a -1 23 1 b-a 2 1 4 T -cos³x sin ²x 1 -2 - e b+ a e 3-b - 1 2 NO - 1 1 -1 O 2 1 013 4 1 خدم برد…

A:

Q: 10. Solve algebraically for 0<x < 2n . 2 cos? x - sin x = -1 sin? x = 2 cos x - 2 a. b. 2. d. 2cos?…

A: The given equation,d) 2cos2x+3cosx+1=0 ; 0≤x≤2π

Q: 2 sin@ cos e-13 sin e= 0 %3D

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Q: -심슨 (005년들 - 1) = 8월 (10000) cos 8A W²t W G(W) = -4A 84 w²z 2 sin we 4 AT sin we Wt 4 2 1 agctu 2A 를…

A:

Q: 7. y = cos`x sin'x %3D 3 A. – 4 cos x sin x B. – 2 sin sin 2x 3 2 C.- 4 cos´x + sin' D.- 2 sinx cos…

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Q: Question 17 Evaluate D3(sinx – 4e) (A) -sin x-32е2х B sin x-32ex -cos x-32 e2x D cos x-32 e?x

A: Solution

Q: 2 cos 0 d 1 - sin A

A: We can find the integration as below.

Q: 2n 1+cos e 6r2 cos e drde

A: This is the double integration

Q: 1 1 1 cos a + cos 3a Cos a + cos 5a 1 Cos a + cos 7a +.... + cos a + cos(2n + 1)a 1 cosecaftan(n +…

A: Given that, We have to prove that, Consider the nth term of the left-hand side, By using the…

Q: = 29. A solution to the trigonometric equation cos x C. x = 2 D. x = x= 1/72. -is A. x = 3 B. x = =…

A: Value of cos(2π/3) is -1/2

Q: 10. Find all solutions of the following equation in the interval [0,27). 2 sin x-2+ cos x Зл 4л 11л…

A: Given equation is: 2sin2x=2+cosx

Q: 1 -³ e"/ cos? e ,? dr sin@de ý do = x 32na X = ?

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Q: 1/2 sin e cos (cos a cosec 0) de TC (1-cos a).

A: Note that we have to show that the integral value is  π2(1 - cosα).

Q: ー49 a+ 22ト7 40 +3)Y-(sin 32) (Cos 2) +e

A:

Q: 2ä + 2i + x =1 with x(0) = 0 and ¿(0) = 2 Answer: x(t) = 1+ 3e-0.5t sin 0.5t – e-0.5t cos 0.5t

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Q: 21. The general solution of 2 cos2 x – sin a -2 =0 is of the form x = An, b + 2nn, +2rn, n EI. The…

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Q: 1.4 = 0.9062 x Cos (1-√³x) dx = 0-6034 How?

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Q: 7/2 sin e cos (cos a cosec 0) d0 TC (1-cos a) 2 -Cos Te/2-

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Q: 1-2 -1 2 3 1 b-a 2 1 4 E -Cos²x sin 2x 1 -2 - e b+ a e 3-b - 1 2 o 2 -1 O 1 -1 2 e 1 943 O 3 1…

A: Matrix addition is possible if the order of the matrices is same  Matrix subtraction is possible if…

Q: 8. Solve: a sin() = { b 2 cos(a +) +1=0 on <a << 3 algebraically. on 0<a <10 using technology. %3D

A: 8.a) sinx5=23 on 0&lt;x&lt;10πb) 2cosx+π4+1=0 on π&lt;x&lt;3π

Q: d (2 - sin 0 cos 0 2 sin 0 1 | a Show that de cos? 0 2 - sin 0 b Hence find the maximum and minimum…

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Q: Зл ,2n) then tg 2 1 If α te( V1- cos“(a – n) + a)+ = 0. 3n – 2a sin(5n + a) 1- sin 2

A: We have to prove the trigonometric equation.

Q: 1. True or False a. The output of the cotangent function is always a number between-1 and 1. b.…

A: As per our company guidelines we are supposed to answer only first three sub-parts. Kindly repost…

Q: Evaluate: D°(sin x- e20) A -sin x - 32e* B sin x - 32e2 © -32- e D cos x - 32e2

A:

Q: (-9)" (2n)! n=0 (a)e³ (b) cos 3 (c) co (d) sin 3 (e) None

A: The given series is ∑n=0∞(-9)n(2n)!

Q: 0ダーツー ゴリ=37%+ e ジャンー のジュリ= cosy cos (x) +38in2x

A: We are entitled to answer one question from the multipart. Please resubmit the question which you…

Q: 1/2 TC sin 8 cos (cos a cosec 0) de (1-cos a). /2-a

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Q: 5 35 sin? 0 cos50 de -2 S(x e* – tan x)dx -3

A: We are entitled to solve only one question at a time and up to 3 sub-parts only. Given - ∫0π235…

Q: -1 -2<x< - 1 0 -1<x<1 1<x<2 nswer: f(x) = a + Tin COS ... COS n=1 sin T²n² O sin () COS

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Q: (1/2 sin e cos 1 (cos a cosec 8) de (1-cos a ||

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Q: 19. Given 0 <0 < 2T, solve 2 cos² 0 +3 sin 0 = 3. ○ 등, 똥 6 6 ○ , 풍,풍 ○ , 풍, 똥 5w 6 ○ 풍, 풍 11.

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Q: Question in Image.

A: First, we write 4pi/3 using its reference angle. Since 4pi/3 is in the third quadrant, there sin is…

Q: 1. Solve the linear equations below on the interval 0 < 0 < 2n. Show ALL your work!! 2 cos(2x) =-V3…

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Q: (5e" + 6x + 5 cos z)da

A: The solution is given below

Q: (g) The sum of two sinusoidal functions is sinusoidal. (h) sin(ß²) + cos(3²) = 1, for all values of…

A:

Q: 8. and A e [0, 180°]. Find sin2A 17 1. Given that cos A =-

A: Topic:- trigonometry  Note:- as per our guideline if more than one question uploaded than only first…

Q: 1/12 216 sin (6x) dx Evaluate 7/18 V1-2 cos (6x)

A:

Q: (-9)" (2n)! n=0 V3 (c) cos (a)e³ (b) cos 3 (d) sin 3 (e) None a b d e

A: Solve by series sum

Q: A violin string produces a vibration u(x,t)=a sin(2t-x/ 137). cos(A-t)+b sin(14t-x / 137). cos(E-t)…

A:

Q: e20 A cos 20 + i sin 20 B (cos e +i sin 0) (cos 0 – i sin 6) B D cos 20 - i sin 20 2.

A:

Q: 4. (a) 5e-2' cos 3t (b) 4e-5t sin t

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Q: 12. Find all values of 0 in the interval [0, 2n) that satisfy the equation: cos 20 + cos 0 = 0

A: We need to find value of θ.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.