Topic
Q:
Question
Evaluate the following limit using L'Hospital's rule.
Enter an exact answer.
\[ \lim _{x \rightarrow \infty} \frac{-x+7}{2 x^{2}-3 x-11} \]
Provide your answer below:
\( \lim _{x \rightarrow \infty} \frac{-x+7}{2 x^{2}-3 x-11}=\square \)
Q:
\begin{tabular}{l} Question \\ Evaluate the following limit using L'Hospital's rule. \\ \( \qquad \lim _{x \rightarrow \infty} \frac{-5 x^{2}+9 x+20}{4 \ln \left(x^{5}\right)} \) \\ Enter an exact answer. \\ Provide your answer below: \\ \( \qquad \lim _{x \rightarrow \infty} \frac{-5 x^{2}+9 x+20}{4 \ln \left(x^{5}\right)}=\square \) \\ \hline\end{tabular}
Q:
Question
Evaluate the following limit using L'Hospital's rule.
Enter an exact answer.
\[ \lim _{x \rightarrow-3} \frac{-6 e^{x+3}+6}{\ln (3 x+10)} \]
Provide your answer below:
\( \lim _{x \rightarrow-3} \frac{-6 e^{x+3}+6}{\ln (3 x+10)}=\square \)
Q:
ind from the first principles, the gradie
functions of the following curves
\( y=5 x+4 \quad y=x^{3}+x^{7} \)
Q:
\begin{tabular}{l} Question \\ Consider the function \( f(x) \) below. Over what open interval(s) is the function decreasing and concave up? Give your answer \\ in interval notation. \\ \( \qquad f(x)=\frac{x^{4}}{4}+\frac{13 x^{3}}{3}+20 x^{2}+36 x-6 \) \\ Enter \( \varnothing \) if the interval does not exist. \\ Provide your answer below: \\ \hline\end{tabular}
Q:
nd from the first principles, the gradi
functions of the following curves
\( y=3 x+4 \)
Q:
Find from the first principles, the gradi
functions of the following curves
\( y=3 x+4 \)
\( y=x^{3}+x^{2} \)
Q:
a) \( \int \frac{2 d x}{\sqrt{4-9 x^{2}}}= \)
Q:
\( \frac{d^{2} y}{d t^{2}}+3 \frac{d y}{d t}+2 y=t^{3}+t^{2}+3 \begin{aligned} \text { when } t & =0 \\ y & =0 \\ \Delta y & (0)=0\end{aligned} \quad \begin{aligned} \frac{d y}{d t} & =1\end{aligned} \)
Q:
\( \left. \begin{array} { l } { 100 \frac { d ^ { 2 } y ( t ) } { d t ^ { 2 } } + 5 \frac { d y ( t ) } { d t } + 4 y ( t ) = \frac { d x ( t ) } { d t } } \end{array} \right. \)
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