Question

Consider the following.\\ $\lim_{x \to 0^+} 9x^2 \cot(x)$\ (a) Describe the type of indeterminate form (if any) that is obtained by direct substitution.\ $ \frac{0}{0} $\ $ \frac{0}{\infty} $\ $ \frac{\infty}{0} $\ $ 0 \cdot \infty $\ $ 1^\infty $\ $ 0^0 $\ $ \infty - \infty $\ $ \frac{\infty}{\infty} $\ not indeterminate\ (b) Evaluate the limit, using L'Hôpital's Rule if necessary. Use a graphing utility to graph the function and verify the result. (If the limit is infinite, enter '$\infty$' or '$-\infty$', as appropriate. If the limit does not otherwise exist, enter DNE.)

          Consider the following.\\
$\lim_{x \to 0^+} 9x^2 \cot(x)$\
(a) Describe the type of indeterminate form (if any) that is obtained by direct substitution.\
$ \frac{0}{0} $\
$ \frac{0}{\infty} $\
$ \frac{\infty}{0} $\
$ 0 \cdot \infty $\
$ 1^\infty $\
$ 0^0 $\
$ \infty - \infty $\
$ \frac{\infty}{\infty} $\
not indeterminate\
(b) Evaluate the limit, using L'Hôpital's Rule if necessary. Use a graphing utility to graph the function and verify the result. (If the limit is infinite, enter '$\infty$' or '$-\infty$', as appropriate. If the limit does not otherwise exist, enter DNE.)

Consider the following.

limx → 0^+ 9x^2 cot(x)(a) Describe the type of indeterminate form (if any) that is obtained by direct substitution.(0)/(0)(0)/(∞)(∞)/(0)0 ·∞1^∞0^0∞ - ∞(∞)/(∞)not indeterminate(b) Evaluate the limit, using L'Hôpital's Rule if necessary. Use a graphing utility to graph the function and verify the result. (If the limit is infinite, enter '∞' or '-∞', as appropriate. If the limit does not otherwise exist, enter DNE.)

Added by Jonathan D.

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