I was doing an assignment and the middle 2 questions are l'Hôpital's rule questions and we haven't even done this in class yet. These are 1 or 2 chapters away yet we are expected to do them and I have no idea how to do these because we haven't learned yet so I was hoping someone here can help me.
First question:
An incorrect use of l'Hôpital's rule is illustrated in the following limit computation. Explain what is wrong and find the correct value of the limit.
$\lim_{x\to\pi/2} \frac{\sin(x)}{x} = \lim_{x\to\pi/2} \frac{\cos(x)}{1}=0$
Second question is:
Find $\lim\limits_{x\to-\infty} xe^x$ using l'Hôpital's rule. Using this information does the function $xe^x$ have a horizontal or vertical asymptote? state the equation of the asymptote.
I have done about 15 pages worth of questions and some I knew because I studied extra things on spare time but these are just hard.