How do you evaluate the limit $\frac{2^{x} + sin x}{x^{4}}$ $(2^x+sinx)/x^4$ as x approaches $0$ $0$ ?

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Answer 1 · 2016-08-08T12:28:10

$\infty$ $oo$

Let's focus on the numerator first.

$lim_(xrarr0)(2^x + sin(x)) = 2^0 + sin(0) = 1$

Overall limit is:

$lim_(xrarr0)1/(x^4) = oo$

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