# Thread: How do you evaluate a limit

1. ## How do you evaluate a limit

How do you evaluate a limit

2. Say this limit equals L. Now take the natural log of the limit and of L. Use log rules to bring the exponent in front and then notice that you get infinity/infinity if you try to apply the limit. Use L'Hopitals rule and you should get your answer.

3. Alternatively, $\frac{5x-1}{5x+3} = \frac{5x+3-4}{5x+3} = 1 - \frac{4}{5x+3}$

And use the fact that $t^{5x+2} = t^{5x+3-1} = t^{5x+3} \cdot t^{-1}$ and that $\left(1 + \frac{a}{f(x)}\right)^{f(x)} \rightarrow e^a$ as x goes to infinity and f(x) goes to infinity.