Topic
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.
Q:
You go to the doctor and he gives you 15 milligrams of radioactive dye. After 12 minutes, 7.75 milligrams of
dye remain in your system. To leave the doctor's office, you must pass through a radiation detector without
sounding the alarm.
If the detector will sound the alarm if more than 2 milligrams of the dye are in your system, how long will
your visit to the doctor take, assuming you were given the dye as soon as you arrived?
Give your answer to the nearest minute.
You will spend
Q:
Evaluate the following limit using L'Hospital's rule.
\[ \lim _{x \rightarrow 0^{+}}(\cos (6 x))\left(\frac{1}{5 x^{2}}\right) \]
Q:
The fox population in a certain region has a continuous growth rate of 7 percent per year. It is estimated
that the population in the year 2000 was 22000 .
(a) Find a function that models the population \( t \) years after 2000 ( \( t=0 \) for 2000).
Hint: Use an exponential function with base \( e \).
Your answer is \( P(t)= \)
(b) Use the function from part (a) to estimate the fox population in the year 2008.
Your answer is (the answer must be an integer)
Q:
Question
Evaluate the following limit using L'Hospital's rule.
\[ \lim _{x \rightarrow 0^{+}}\left(\frac{1}{8 x}\right)^{\left(\frac{1}{6 \ln (7 x)}\right)} \]
Q:
Question
Evaluate the following limit using L'Hospital's rule.
\[ \lim _{x \rightarrow 0^{+}}(5 x)^{\left(\frac{1}{8 \ln (8 x)}\right)} \]
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