Home » Blog » Compute the limit of the given function Compute the limit of the given function by RoRi December 25, 2015 Evaluate the limit. First, we pull an out of and an out of to write Then we have Related
![\[ \lim_{x \to +\infty} \frac{\log (a + be^x)}{\sqrt{a+bx^2}}. \]](http://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-8e50e4bd8f639fdfff7b901df2e563ab_l3.png "Rendered by QuickLaTeX.com")
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to write![\[ \frac{\log(a+be^x)}{\sqrt{a+bx^2}} = \frac{\log((e^x)(ae^{-x} + b)}{x \sqrt{ax^{-2} + b}} = \frac{x + \log(ae^{-x} + b)}{x \sqrt{ax^{-2} + b}}. \]](http://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-63b08cd0d21e2086fe598f8564e3c765_l3.png "Rendered by QuickLaTeX.com")
![\begin{align*} \lim_{x \to +\infty} \frac{\log (a + be^x)}{\sqrt{a+bx^2}} &= \lim_{x \to +\infty} \frac{x + \log(ae^{-x} +b)}{x\sqrt{ax^{-2} + b}} \\[9pt] &= \lim_{x \to +\infty} \left( \frac{1}{\sqrt{ax^{-2} + b}} + \frac{\log(ae^{-x} + b)}{x \sqrt{ax^{-2} + b}} \right)\\[9pt] &= \frac{1}{\sqrt{b}} + 0 &(\text{Theorem 7.11})\\ &= \frac{1}{\sqrt{b}}. \end{align*}](http://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-50a31dfb2c175c3a844f248a183b3199_l3.png "Rendered by QuickLaTeX.com")
out of and an out of to write