# How do you evaluate the limit (2^x+sinx)/x^4 as x approaches 0?

Aug 8, 2016

$\infty$

#### Explanation:

Let's focus on the numerator first.

${\lim}_{x \rightarrow 0} \left({2}^{x} + \sin \left(x\right)\right) = {2}^{0} + \sin \left(0\right) = 1$

Overall limit is:

${\lim}_{x \rightarrow 0} \frac{1}{{x}^{4}} = \infty$