Science:Math Exam Resources/Courses/MATH100/December 2014/Question 08 (d)

MATH100 December 2014

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Question 08 (d)
Let $f(x)={\frac {\log(x)}{\sqrt {x}}}$. Note $\log(x)$ is the natural logarithmic function, also denoted $\ln(x)$ (d) Find the vertical asymptotes of the graph of $f(x)$, if they exist. Justify your answer.

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Hint
What $x$ values should be checked?

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Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. Since the function is defined for all $x>0$ the only possible vertical asymptote is as $x\rightarrow 0^{+}$. Now, as $x\rightarrow 0^{+}$ the numerator becomes large and negative, while the denominator becomes small and positive. Hence $\lim _{x\rightarrow 0^{+}}{\frac {\log x}{\sqrt {x}}}=-\infty$ This asymptote at $x=0$ is the only vertical asymptote.

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