Let f(t) = 00 n=1 2 6n³ + 3n¹3 -cos(nt).

Q: 13. To evaluate f 3cos*x-1 dx. the integrand can be transformed to 1-sin2x a. [(3cos x+ csc²x)dx b.…

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Q: Part 1: 1 1. S *(In x)3 dx 2. Se3x cos x dx 3. S(1 + x²)e-*dx 4. So x²e*dx

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Q: Show that 1 Σ (z – n)2 cosec² (z) 8.

A: As we all know the theorem which states that, For z∈ℂ\ πℤ 1sinz=∑n=-∞∞-1nz-nπ=1z+2z∑n=1∞-1nz2-n2π2…

Q: Evaluate each of the following: (a) /" In(x) dx

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Q: Prove that sinh−1 t = ln(t + √t2 + 1 ).

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Q: Evaluate √x² cos (2³) de dx

A: The given integral is: I=∫x2cosx3dx    ...1   As we know the common integral. ∫cosxdx=sinx+C And…

Q: Find z(t) for X(s) = 8-2 %3D $(s+ 1)(+9) Select one: O a.z(t)3D-86(0) + 금etu(e)-뷰.e 2.cos3t. u(t) +…

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Q: d Prove that (x") = n x"-1 dx

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Q: n/2 1+2cos x Q:Evaluate: dx. (2+cos x)*

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Q: C: Proof that ( a) L (cos²t - sin²t) S s² + 36

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Q: Prove that Jn (x) X good dx=1. n

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Q: 7. Prove that d dx [cos ¹ x] = = 1 √1-x² x2

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Q: f (x) = { ₂x² (²/²) ² 2=1 Coso f(z) dz= ? 23

A: We have to calculate

Q: Simplify (if necessary) then 2 Compute: y" +Éy' for a2 y(z) = rar (zx+ cosx')] [6(cosh2x- sinh2x)] d…

A: given yz=∂2∂x∂zz2x+cosx96cosh2x-6sinh2x36cos2πxddx3x2 claim- if necessary simplify then compute the…

Q: Show that cos A x e 2 *,x2 0. %3D

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Q: Find y = 223 [tan(3r+1)] 2° + ry – y5 = 8x2 = (x + 3)² (x² – 2x) -

A: The Product Rule : The Product Rule says that the derivative of a product of two functions is the…

Q: Find the greatest value of F (x)= | (6 . cos t - 2 sin t) dt 5 7/3 in the interval [5/3,7 t/ 4|.

A: Fro the given problem: Fx=∫5π/3x6cost-2sintdt Now solve the above definite integral,…

Q: The number of houses that can be served by a water pipe varies directly as the square of the…

A: Given that, The number of houses that can be served by a water pipe varies directly as the square of…

Q: Solve using an integral cos²(x) + 2cos²( cos³(x) .dx

A: Evaluation of the integral

Q: dx Evaluate: /9 – x² A @ sin -1 +C .3. 1 3 sin +C 3. B

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Q: Show that J−1/2(x) = √2/πx co

A: Bessel functions are a family of mathematical functions that arise in many areas of physics and…

Q: /2 Prove that 5x1² |π x J1,2 (2x) dx = 1.

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Q: b) S x² cos(2 x³)dx

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Q: Evaluate L{3 (t² – 1) sin (2t) + 7et cosh (4t)}

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Q: Linearize f(x) = 5 cos x about x = pi over 2. f(x) = -5x

A: linearization around x=a is given by :L(x)=f(a)+f'(a)(x-a)