1. Evaluate f{(t² e2t + sinh2t)}

Q: Let f(x) = (sin(x))*. Find the value of (a) 1 (b) 2 (c) 2 (d) 2 (e) 0

A: The given function is fx=sinxx. To find the value of f'π2, first take the logarithmic of fx=sinxx on…

Q: Find f. f"'(t)  = t   - √t

A: To find f"(t) we integrate f"'(t)

Q: Show that (a) · J-1;2(x) = 2 Vлx cos x

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Q: 13x Find the derivative of the function y = 2 tan¬1 (5x ). (Use symbolic notation and fractions…

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Q: If SeF dr = [c(-5x + 3y² ) dx + (x³y) dy, what is F? %3D F =

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Q: c. _h(x) = e¯³(sin(x) + 2x); only quotient rule

A: To solve the following using quotient rule

Q: 4 (t) = -5 sin t + 8sec?t – 8 csct cot t + 4et + - 1+

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Q: 2. 1 Evaluate the definite integrals below. Use u-substitution when appropriate. 4 5 3el/x (a) (b) |…

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Q: Let f (t) = et sin 8t Part (a) Find L{f(t)}

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Q: Evaluate L{t°e! e3(1 – t) 3e-t sin (4t - 2) 2) + t2 $ (3t)} cos

A: Explanation of the answer is as follows

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

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Q: Solve S(cosa{x – +)<(1 + +) dx -

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Q: V sin2(x32 - 1) dx, with u x32 - 1

A: Consider the integral ∫(√x)sin2 (x3/2 - 1) dx.

Q: )L{sinh(7t) + (2t + 1)U (t – 1)},

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Q: Find the third derivative of f(1)= 2x(x -1)" Oa 18 b.14cos 13 OC16sim Od12

A: we all know that dxndx= nxn-1. and first derivative dfxdx=f'x and second derivative df'xdx=f''x and…

Q: Differentiate the function. H'(z) = H(z) = In c²-2² c²+z²

A: H(z)=lnc2-z2c2+z2

Q: Q2: Derive the following functions sin2x 1. f(x) sec?x 2. f(x) = x²e*²

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Q: Q) prove that (1) -2P xSinx 2.

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: 1. Differentiate. Do not simplify. а. f(0) = 3cos(0*)sin(0³ – 2) b. f(x) = 4x + 25-x² + 2x-1

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Q: ∫((1/t)+6th root of t)dt

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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…