Topic
Q:
Question
Evaluate the following limit using L'Hospital's rule.
\[ \lim _{x \rightarrow 0^{+}} 9 x \tan \left(-2 x+\frac{\pi}{2}\right) \]
Provide an exact answer.
Provide your answer below:
\( \lim _{x \rightarrow 0^{+}} 9 x \tan \left(-2 x+\frac{\pi}{2}\right)=\square \)
Q:
Question
Evaluate the following limit using L'Hospital's rule.
\[ \lim _{x \rightarrow 0^{+}}\left(\frac{1}{9 x}\right)^{\left(\frac{1}{4 \ln (6 x)}\right)} \]
Provide your answer below:
\( \lim _{x \rightarrow 0^{+}}\left(\frac{1}{9 x}\right)^{\left(\frac{1}{4 \ln (6 x)}\right)}=\square \)
Q:
Question
Evaluate the following limit using L'Hospital's rule.
\[ \lim _{x \rightarrow 0^{+}} 3 x^{2} \ln \left(5 x^{3}\right) \]
Provide your answer below:
\( \lim _{x \rightarrow 0^{+}} 3 x^{2} \ln \left(5 x^{3}\right)=\square \)
Q:
\begin{tabular}{l} Question \\ Evaluate the following limit using L'Hospital's rule. \\ \( \qquad \lim _{x \rightarrow 0} \frac{\sqrt{9+19 x}-\sqrt{9+15 x}}{3 x} \) \\ Enter an exact answer. \\ Provide your answer below: \\ \( \lim _{x \rightarrow 0} \frac{\sqrt{9+19 x}-\sqrt{9+15 x}}{3 x}=\square \) \\ \hline\end{tabular}
Q:
\begin{tabular}{l} Question \\ Evaluate the following limit using L'Hospital's rule. \\ Enter an exact answer. \\ \( \qquad \lim _{x \rightarrow 0} \frac{-19 e^{3 x}+19}{4 \sin (2 x)} \) \\ Provide your answer below: \\ \( \lim _{x \rightarrow 0} \frac{-19 e^{3 x}+19}{4 \sin (2 x)}=\square \) \\ \hline\end{tabular}
Q:
\begin{tabular}{l} Question \\ Evaluate the following limit using L'Hospital's rule. \\ \( \qquad \)\begin{tabular}{l}\( \lim _{x \rightarrow 0} \frac{7 \sin (5 x)}{2 \tan (2 x)} \) \\ Enter an exact answer. \\ \( \qquad \begin{array}{l}\lim _{x \rightarrow 0} \frac{7 \sin (5 x)}{2 \tan (2 x)}=\square\end{array} \) \\ \hline\end{tabular}. \\ \hline\end{tabular}
Q:
Question
Evaluate the following limit using L'Hospital's rule.
\[ \lim _{x \rightarrow \infty} \frac{17 x-e^{7 x}}{2 x^{2}+18 x-1} \]
Enter an exact answer.
Provide your answer below:
\[ \lim _{x \rightarrow \infty} \frac{17 x-e^{7 x}}{2 x^{2}+18 x-1}=\square \]
Q:
Question
Evaluate the following limit using L'Hospital's rule.
\[ \lim _{x \rightarrow \infty} \frac{x-e^{13 x}}{5 x^{2}-11 x+8} \]
Enter an exact answer.
Provide your answer below:
\( \lim _{x \rightarrow \infty} \frac{x-e^{13 x}}{5 x^{2}-11 x+8}=\square \)
Q:
\begin{tabular}{l} Question \\ Evaluate the following limit using L'Hospital's rule. \\ \( \qquad \lim _{x \rightarrow 0} \frac{-4 x+4 \sin (x)}{4 x^{3}} \) \\ Enter an exact answer. \\ Provide your answer below: \\ \( \qquad \lim _{x \rightarrow 0} \frac{-4 x+4 \sin (x)}{4 x^{3}}=\square \) \\ \hline\end{tabular}
Q:
PRINCIPIO DE SUSTITUCION
\( \begin{array}{ll}\text { 4. Evaluar los siguientes límites: } \\ \begin{array}{lll}\text { 1. } \lim _{x \rightarrow 2} \frac{x^{2}-3 x+6}{5 x-1} & \text { 3. } \lim _{x \rightarrow 4} \sqrt[3]{x+4} & \text { 4. } \lim _{x \rightarrow 4} \sqrt{\frac{x_{2}-1}{x-1}} \\ \text { 5. } \lim _{x \rightarrow 0} \frac{4-\sqrt{16+x}}{x} & \text { 6. } \lim _{x \rightarrow 1} \frac{x^{3}-2 x^{2}+x}{x-1} & \text { 7. } \lim _{x \rightarrow 4} \sqrt{\frac{25-(x+1)^{2}}{5+(x+1)}} \\ \text { 10. } \lim _{x \rightarrow 3} \frac{\left(x^{2}-9\right)\left(x^{3}+2 x^{2}-3 x\right)}{x^{2}-3 x} & \end{array}\end{array} \$ \begin{array}{l}\end{array} \)
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