Science:Math Exam Resources/Courses/MATH110/April 2013/Question 03 (b)

MATH110 April 2013

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Question 03 (b)
Let $f(x)={\frac {\sin(x)}{e^{x}}}$ on the interval $[0,\pi ]$. In this question you will sketch this function. (b) Find the vertical asymptotes of ƒ, if any exist.

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
Recall that $\displaystyle a$ is a candidate for a vertical asymptote only if $\displaystyle f(x)$ has a discontinuity at $\displaystyle a$, so that there is a chance that $\displaystyle f(x)$ tends to $\displaystyle \infty$ or $\displaystyle -\infty$ as $\displaystyle x$ approaches $\displaystyle a$.

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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. The functions $\displaystyle \sin(x)$ and $\displaystyle e^{x}$ are both continuous everywhere. Further, the function in the denominator, $\displaystyle e^{x}$, is never 0. Hence $\displaystyle f(x)$ is continuous everywhere and thus there are no vertical asymptotes.

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