Math  /  Calculus

QuestionUse a calculator to graph the function and estimate the value of the limit, then use L'Hôpital's rule to find the limit directly. limx0+ln(x)sin(x)\lim _{x \rightarrow 0^{+}} \frac{\ln (x)}{\sin (x)}
DNE

Studdy Solution
Evaluate the limit based on the analysis: - As x0+x \rightarrow 0^{+}, ln(x)\ln(x) becomes very large negative, and sin(x)\sin(x) becomes very small positive. - Therefore, ln(x)sin(x)\frac{\ln(x)}{\sin(x)} \rightarrow -\infty.
Thus, the limit is:
limx0+ln(x)sin(x)= \lim_{x \rightarrow 0^{+}} \frac{\ln(x)}{\sin(x)} = -\infty
The estimated and calculated value of the limit is:
\boxed{-\infty}

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