$(12$ points$)$

For this problem, evaluate the limit if it exists, or state why a particular limit does not exist. If the limit is infinite, specify the sign or $-.$ Show all work and state any theorems used, justifying why you have met the conditions of any theorems you use.

$($a$)\underset{x1}{lim}\frac{x^2-1}{x^2-x}$

$($b$)\underset{t0}{lim}\frac{1-t}{t^2}$

$($c$)\underset{x{0}^{+}}{lim}x*ln(x)$

$($d$)\underset{x0}{lim}\frac{e^x-1}{sin(x)}=$