Topic
Q:
Question
Evaluate the following limit using L'Hospital's rule.
\[ \lim _{x \rightarrow 0^{+}}\left(\frac{-10}{x}+\frac{2}{\sin (5 x)}\right) \]
Q:
\( \begin{array}{l}\text { Determine el tipo de discontinuidad } \\ \text { que presente la siguiente función en } \\ \text { el punto } x=1\end{array} \)
\[ f(x)=\left\{\begin{array}{ll}x & \text { si } x \leq 1 \\ 2 & \text { si } x>1\end{array}\right. \]
Q:
Question
Evaluate the following limit using L'Hospital's rule.
\( \lim _{x \rightarrow \infty}(-8 x)^{2} e^{-3 x} \)
Q:
Question
Evaluate the following limit using L'Hospital's rule.
\[ \lim _{x \rightarrow \infty} 4 x^{5} \cos \left(\frac{1}{3 x^{5}}+\frac{\pi}{2}\right) \]
Provide an exact answer.
Q:
2. Dadas las funciones \( f(x)=x^{4}-2 x \) y \( g(x)=5 x+3 \), encuentra la derivada de \( h(x)= \)
\( f(x) \cdot g(x) \).
Q:
Son correctas las siguientes
evaluaciones para saber si la función
es continua en el intervalo \( (2,3] \)
\( \mathrm{f}(2,3) \)
\( \lim _{x \rightarrow 3^{-}} f(x) \)
Q:
Find the integral.
\( \int 4(2 x+5)^{3} d x \)
Q:
Question
Evaluate the following limit using L'Hospital's rule.
\[ \lim _{x \rightarrow 1}\left[\frac{1}{3 \ln (x)}-\frac{5}{15 x-15}\right] \]
Q:
Question
Evaluate the following limit using L'Hospital's rule.
\[ \lim _{x \rightarrow 0}\left[\frac{1}{8 e^{x}-8}-\frac{1}{8 x}\right] \]
Q:
Question
Evaluate the following limit using L'Hospital's rule.
\( \lim _{x \rightarrow \infty}(5 x)^{\frac{5}{x}} \)
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