1-Find the Cauchy principle value (showing details): J_co (7*+5x²+4)' cos(4x) dx 8.

Q: d -1 ) Prove that cos 1(x) : dx V1-1

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Q: Prove that (1+i)" +1(1-i)" = 2 cos %3D

A: We will solve the following

Q: Show that T (1-i) cos- +isin- 40 40 (81-8√3) 6 10 = -√2

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Q: trace the equation in 3 -dimension

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Q: 3. Differentiate a) (x3+2x)e(2x+1) b) cosxsinx

A: Topic = Derivative

Q: Evaluate sin (3x) cos (6x) dx Select one: cos(9r) A cos(3r) tC 18

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Q: Determine if the setsin² {sin²x, 1-cos(2x)} is linearly dependent or linearly independent on I =…

A: Let B={sin2x,1-cos(2x)}.

Q: If the root of C.E. are (-2, -2, 0, ±2i) then yH = (a) A + Be-2x + Be-2* + Dcos2x + Esin2x (b) A +…

A: We have to find the following

Q: 1 |Leax sin(bx)] eax [a sin(bx) – b cos(bx)]+ C * Using the formula dx = ах a² + b². Sie [e-8x…

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Q: Q2-By using the formula cos(A – B) = cosAcosB + sinAsinB & sin(A – B) = sinAcosB - cosAsinB…

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Q: Show that the equation 2x + cos(x) = 1 has exactly one root. (IVT and Rolle's Theorem)

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Q: 4sinx •cotx / cos2x + 1

A: You know:

Q: Evaluate: e* cos (7e*)cos (4e*) dx (A sin (3e*) +sin (11e") +c - sin (11e*)+C - sin 6. 22 ® -cos…

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Q: ,2 Compute x² cos(x³ + 3) dx

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Q: 6) Use Linear Property to find ( 1- 3 x4)' A) (1- 3 x4) %3D B) – 4x3 C) - 2 D) - 12 x3 7) Use…

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Q: Q2-By using the formula cos(A – B) = cosAcosB + sinAsinB & %3D sin(A – B) = sinAcosB- cosAsinB…

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Q: 2- Exercise: Evaluate a) L{4x? – 3 cos(2x) +5e*} b) L{4+sin (x) – e**}

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Q: Find So Cosx (x² + 1)² - ex

A: We shall be using basics of residue calculus to evaluate this integral

Q: Use the identity cos alpha cos beta = 1/2[cos(a-b)+cos(a+b)] to rewrite 2cos3xcos2x as a sum of trig…

A: The given identity