L'Hospital's Rule (College Board AP® Calculus AB): Exam Questions

Which of the following limits could you not attempt to evaluate using L'Hospital's rule?

If $f^{\text{'}}\left(x\right)=\sin x-1$ and $g^{\text{'}}\left(x\right)=2$ for all $x$, and if $f\left(0\right)=g\left(0\right)=0$, then $\underset{x\to 0}{\lim }\frac{f\left(x\right)}{g\left(x\right)}$ is

$\underset{x\to \frac{3\pi }{2}}{\lim }\frac{\sin x+1}{\cos x}$ is

$\underset{x\to 0}{\lim }\frac{\tan 3x}{\sin 5x}=$

$\underset{x\to 0}{\lim }\frac{1-\cos 3x}{1-\cos 7x}=$

If $a\ne 0$, then $\underset{x\to a}{\lim }\frac{x^2-a^2}{x^5-a^5}$ is

$\underset{x\to 0}{\lim }\frac{1-{\cos }^2\left(3x\right)}{{\left(3x\right)}^2}=$

$\underset{x\to 0}{\lim }\left(\frac{1-\cos x}{x\sin 2x}\right)$ is

$\underset{x\to 0}{\lim }x\cot 3x=$

$\underset{x\to 1}{\lim }\frac{\sin \left(\sin \pi x\right)}{x^2-1}$ is