I have trouble with this limit evaluation due to the fractions in it.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\lim_{x \rightarrow 0} \left[3x^5cos\left(\frac{1}{x}\right)\right][/tex]

I assumed that [tex]cos\left(\frac{1}{0}\right) = \infty[/tex] so that limit gives [tex](0 \cdot \infty)[/tex] and is an indeterminate form. As such, I rearrange so that I can use L'Hopital's rule:

[tex]\lim_{x \rightarrow 0} \left[\frac{cos\left(\frac{1}{x}\right)}{\frac{1}{3x^5}}\right][/tex] this becomes [tex]\left(\frac{\infty}{\infty}\right)[/tex] and L'Hopital's rule applies.

[tex]\Rightarrow \lim_{x \rightarrow 0} \left[\frac{\frac{sin}{x^2}\left(\frac{1}{x}\right)}{-\frac{5}{3x^4}}\right][/tex]

Am I correct so far?

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# Homework Help: Evaluating limits

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