Question

Problem on limits with a natural log? I'd like to solve it by hand and having trouble considering I've forgotten most of the log stuff. Also not using L'hopitals rule would be great.
http://imgur.com/ouDyB2p

Answer 1

You don't need any log rules here. L'Hopital's Rule is actually the EASIEST approach to use here.

Recall the following:\[\frac{ d }{ dx } \ln(x) = \frac{ 1 }{ x } + C\]
Similarly because of the chain rule
\[\frac{ d }{ dx } \ln(f(x)) = \frac{ f'(x) }{ f(x) }+C, ~ ~\forall ~x ~\in R ^{+}\]

L'Hopital's rule states the limit of a quotient is equal to the limit of the corresponding derivatives providing the limit does exist. As the derivative of ln(1+x^4) is very easy to calculate you should be able to evaluate the limit quickly.

Answer 2

while solving using L'hospitals rule take the partial derivative of the numerator and denominator but remember that u can use L'Hospitals rule only when limit is of the form 0/0 or