Tema
Q:
Using L'Hospital's rule, determine whether \( f(x) \) or \( g(x) \) given below grows at a faster rate.
\[ \begin{array}{l}f(x)=x^{2}-2 x \\ g(x)=4^{x}-2 x\end{array} \]
Q:
\begin{tabular}{l} Using L'Hospital's rule, determine whether \( f(x) \) or \( g(x) \) given below grows at a faster rate. \\ \( \qquad \begin{array}{ll}f(x)=x \\ g(x)=5 \ln (x)\end{array} \) \\ Select the correct answer below: \\ f(x) grows at a faster rate. \\ g(x) grows at a faster rate. \\ There is not enough information to determine which function grows at a faster rate. \\ \hline\end{tabular}
Q:
\begin{tabular}{l} Question \\ Using L'Hospital's rule, determine whether \( f(x) \) or \( g(x) \) given below grows at a faster rate. \\ \( \qquad \begin{aligned} f(x)=2^{x}+2 x \\ g(x)=5 x^{3}\end{aligned} \) \\ Select the correct answer below: \\ f(x) grows at a faster rate. \\ g(x) grows at a faster rate. \\ There is not enough information to determine which function grows at a faster rate. \\ \hline\end{tabular}
Q:
\[ f(x)=\frac{2 x^{\frac{3}{2}}}{5}-\frac{2 x^{\frac{3}{2}}}{3}-6 \text { over }[0,4] \]
Enter an exact answer. If there is more than one value of \( x \) in the interval at which the maximum or minimum occurs, you
should use a comma to separate them.
Q:
\begin{tabular}{l} Question \\ Using L'Hospital's rule, determine whether \( f(x) \) or \( g(x) \) given below grows at a faster rate. \\ \( \qquad \begin{aligned} f(x)=-4 x^{4}-2 x-4 \\ g(x)=2 x^{3}+x^{2}-x\end{aligned} \) \\ Select the correct answer below: \\ f(x) grows at a faster rate. \\ g(x) grows at a faster rate. \\ f(x) and \( g(x) \) grow at the same rate. \\ There is not enough information to determine which function grows at a faster rate. \\ \hline\end{tabular}
Q:
\begin{tabular}{l} Question \\ Using L'Hospital's rule, determine whether \( f(x) \) or \( g(x) \) given below grows at a faster rate. \\ \( \qquad f(x)=-3 x^{2}-x-1 \) \\ \( g(x)=-x^{3}-5 x-2 \) \\ Select the correct answer below: \\ f(x) grows at a faster rate. \\ g(x) grows at a faster rate. \\ f(x) and \( g(x) \) grow at the same rate. \\ There is not enough information to determine which function grows at a faster rate. \\ \hline\end{tabular}
Q:
Question
Evaluate the following limit using L'Hospital's rule.
\[ \lim _{x \rightarrow 0^{+}}(9 x)^{\sin (4 x)} \]
Q:
Find the integral.
\( \int\left(\frac{2}{x}+2 e^{x}\right) d x \)
Q:
Question
Evaluate the following limit using L'Hospital's rule.
\[ \lim _{x \rightarrow 0^{+}}\left(e^{6 x}+2 x\right)^{\left(\frac{1}{9 x}\right)} \]
Q:
At the beginning of an experiment, a scientist has 228 grams of radioactive goo. After 135 minutes, her
sample has decayed to 14.25 grams.
What is the half-life of the goo in minutes?
Find a formula for \( G(t) \), the amount of goo remaining at time \( t \).
\( G(t)= \)
How many grams of goo will remain after 44 minutes?
You may enter the exact value or round to 2 decimal places.
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