8. The value of f sinh* x cosh³ x dx

Q: For which x value(s) is f(x) = X sin 4x continuous? Explain why.

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Q: tind the derivative using the chfinition +(x) 9x %3D

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Q: Find the derivative of y = In (tanh x).

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Q: 9. f 6 sec¹ xdx

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Q: 18. f(tan 2x + cot 2x)² dx

A:

Q: Excrcise 10. Find the derivative d -7x * [" (t³ + 2) dt dx

A: Given,          ddxx∫57xt3+2dt

Q: Sx² cosh (1-x³) dx

A: Let the given integral be I - I = ∫x2cosh1-x3dx                   ............(1)Let,t = 1-x3…

Q: da Vx(1+ x) 1. 8.

A:

Q: . Evaluate S (-+ 3e* ) dx

A: We have to Evaluate  ∫ {(1/√x) - (2/x) + 3ex} dx = ∫(1/√x) dx - 2 ∫(1/x) dx + 3 ∫ex dx

Q: 10. f sin³x dx

A:

Q: Differentiate. A f(x) : В + Сех f'(x) =

A: Given  f(x) = AB+Cex f'(x) = dAB+Cex-1dx                       ∵1a = a-1

Q: 5. Comparison Test Determine whether the following integrals converge or diverge. dx

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Q: 3 Itanz. secxdx

A: