Question Three

Consider each of the limits below.

$($a$)$ Complete the table for each limit$.$ Write a sentence or two noting what you observe and what the value of the limit seems to be from the table.

$($b$)$ Calculate the limit using L$\text{'}$H$$pital$\text{'}$s Rule. Clearly show all the steps making note of the step$($s$)$ where L$\text{'}$H$$pital$\text{'}$s Rule was used.

$($c$)$ Does the limit you found from the table match the limit you calculated using L$\text{'}$H$$pital$\text{'}$s Rule?

$\underset{x}{lim}\frac{x}{e^x}$

$\backslash$table$[[x,x,e^x,\frac{x}{e^x}$