if the degree of \(P\) is (a) less than the degree of \(Q\text{,}\) and (b) greater than the degree of \(Q\text{.}\) If the answer is infinite, enter "I" below.
(a)
(b)
2.
Evaluate the limit using L’Hospital’s rule if necessary.
\begin{equation*}
\lim_{ x \rightarrow +\infty } \frac{x^{11}}{e^x}
\end{equation*}
Answer:
3.
Suppose that \(f(x) = -5 x^2 + 8\text{.}\)
(A) Find the slope of the line tangent to \(f(x)\) at \(x=-6\text{.}\)
(B) Find the instantaneous rate of change of \(f(x)\) at \(x=-6\text{.}\)
(C) Find the equation of the line tangent to \(f(x)\) at \(x=-6\text{.}\)\(y=\)
Differentiate \(\displaystyle y =\frac{x}{\cos{x}}\text{.}\)
\(y'=\)
8.
If \(f(x) = 5 \cos(3\ln(x))\text{,}\) find \(f'( x )\text{.}\)
Answer:
9.
Consider the function \(f(t) = 9 \sec ^2(t) - 9 t^ { 3 }\text{.}\) Let \(F(t)\) be the antiderivative of \(f(t)\) with \(F(0) = 0\text{.}\) Find \(F(t)\text{.}\)
