E. Evaluate the following. 1. L{e* + cos 6t – ešt cos 6t}

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A: (1) We have to find the exact value of the following -  sin-1sin7π6Since sin-1 and sin together will…

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Q: 40 Зп Given sin(e) , where n<0<. Which of the following is true? 2 41 A csc open parentheses theta…

A: Given sin(θ)=-4041We know thatcosec(θ)=1sinθcosec(θ)=1-4041cosec(θ)=-4140We know that…

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Q: 14. Evaluate L{e" cos(30)}. s-4 A) s - 8s +25 B) s - 8s + 25 4 C) s - 8s + 25 s+4 D) s - 8s +25

A: As we know that the Laplace identity; 1). If Lft=Fs then Leatft=Fs-a  2). Lcosat=ss2+a2   Given:…

Q: 2) Find L{te"sin5t} using two methods. ans: (s+2)2+25

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Q: 9) 5olve For OLO<2M Cose+sin A =1 2.

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Q: 5. Solve the following IVP: sin(t) y = -4 cos*(t), y(;) = cos(t) y' + 0.

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Q: V3 d the exact value of cos(ø – 8), given that cos(4) = , and cos(8) = -, where o is in the t…

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Q: Evaluate: L{cos(3+2t)} s cos32sin3 A s²+4

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Q: (/2 x cos" x dx, when n> 1, show that Jo If In п(п - 1)1,-2 — 1 In [Hint: cos" x= cos? x.cos"-2 x…

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Q: Evaluate the followings: (1) S" e-2x x² dx (2) S cos® 0 de

A: Since the question has multiple questions. But according to guidelines we will solve the first…

Q: S 17x cos (In(x)) dx =? .3 COS A) 30 B) 20

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Q: 4) Find the value of cos(1.74) from the following table oot x y = sin(x) Hint: dy dx 1.7 0.9916…

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Q: Evaluate L{e (sin3t + cos 5t)}. 3. s+5 A. +. (s+5)+9(s+ 5)+25 3. s-5 В. (s-5)-9 (s-5) +25 s+5 C.…

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Q: -24-4s e S COS os(28) – 7 sen(28) cos s+6 s2 + 49

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Q: Evaluate L{e" (sin5t – cos3t)} . 3 s+5 А. (s+5)° +9 2 (s+5)° +25 3 s - 5 В. s-5) –9 (s-5)* +25 3 s+5…

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Q: 4. g(t) = e³t + cos(6t) – e³ªcos(6t) 5. f(t) = tcosh(3t) 6. h(t) = t²sin(2t)

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Q: s+3 is equal to s2 – 6s + 45 | A e3tcos6t В e3t (cos6t + sin6t) © e-3t(cos6t + sin6t) D e3t(cosh6t +…

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Q: Suppose m and n are constants and m #n. Evaluate sin(mx) cos(nx) dx-

A: To evaluate we first multiply and divide by 2 the given function.  Then use the formula: 2(sin(mx)…

Q: 7T What is a possible value of arccos ? Answer must be in COS 6. 0 <0< 2n. 6. 11T 6. 6. O 7T 4

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Q: 4. Evaluate the following in terms of Gamma function sin (4r) cos (2r)dr

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Q: Solve the following for 0 s x s 2n. cotx cos² x = 2cotx

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Q: Find y' (y prime) and y" (double prime)y = cos(x2)

A: To determine the expressions for the first and second derivatives of the given composite function

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A: we use the formula ddx(ax)=ax lna

Q: 1. L{e³t+cos 6t - e³t cos 6t}

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Q: Find L {e 2°cos3t}. -2t

A: The Laplace transform of  a function is Fs=Lft. Given ft=e-2tcos3t. Apply the transformation rule…

Q: for 0 (0° < 0 < 2n) in the equation 2sin e cos e - sin e - 2cos 0 + 1 = 0.

A: Given that, 2sinθcosθ-sinθ-2cosθ+1=0. We know that, sinθ=sinα⇒θ=nπ+-1n+α       α∈-π2,-π2…

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Q: 3. Calculate L {e=# cos(2t – 7)} COS

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Q: Find L(e³t cos 2t)

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Q: 1 Evaluate Le' cos 2t +÷sinh 2t

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Q: 22: Evaluate Sea s cos²(y s) ds.

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Q: Q3. Calculate L{e-ª cos(2t – 1)} COS

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Q: (2)so3ə]E=l2], (22436)9]dz [e cos(z) (z–2)3 Iz|=3

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Q: 8. Find all values of 0, if 0 is in the interval [0°, 360°) and cos 0 V3 2

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Q: with B in Q3 find sin (A B). 13 with A in 0l and cos B

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Q: 25. cos² z dr CoS

A: Given that: ∫cos2x.dx

Q: 3. Find the O to the nearest degree if and with if cos 0= -0.8910 and Q II with 0<0<360°.

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