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# Limits, L'Hopital's Rule and Integrals

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1. Evaluate 2)
2. Differentiate the function f(x) = ln(2x+3)
3. Find lim x&#61664;&#8734; (e2x / (x + 5)3). Apply L'Hopital's rule as many time as necessary, verify your results after each application.
4. Evaluate &#8747;xsinh(x)dx

See attached file for full problem description.

https://brainmass.com/math/integrals/limits-l-hopital-s-rule-and-integrals-141362

#### Solution Preview

1. Int [ dt/(t+1)^2 ] Let (t+1) = x; hence, dt = dx

= Int [ dx/x^2 ] = -1/x

Now apply the limits; when t=1, x = 2 ; t=2, x=3

Hence, integral = 1/2 - 1/3 = 1/6
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2. f(x) = ln (2x+3)

...

#### Solution Summary

Limits, L'Hopital's Rule and Integrals are investigated.

\$2.19

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