1. Limits and Continuity

Find the limit.

$\lim_{x\rarr2}\frac{x^2-7x+12}{x-3}$

Find the limit.

$\lim_{x\rarr-2}\frac{x^2-5x-14}{x+2}$

Find the limit.

$\lim_{x\rarr-\pi}\frac{\sin x}{x}$

Find the limit.

$\lim_{x\rarr3}\frac{\sqrt{x}-\sqrt3}{x-3}$

Find the limit.

$\lim_{x\rarr0}\frac{\sqrt{x+1}-1}{x}$

Find the limit.

$\lim_{x\rarr5}\frac{x-5}{\sqrt{x}-\sqrt5}$

Find the following limits or state that they do not exist. Assume a, b , c, and k are fixed real numbers.

lim h→0 √16 + h − 4 / h

Find the following limits or state that they do not exist. Assume a, b , c, and k are fixed real numbers.

lim x→4 1/x−1/4 / x − 4

Find the following limits or state that they do not exist. Assume a, b , c, and k are fixed real numbers.

lim h→0 (5 + h)^2 − 25 / h

Find the following limits or state that they do not exist. Assume a, b , c, and k are fixed real numbers.

lim x→4 3(x − 4)√x + 5 / 3 − √x + 5

Find the following limits or state that they do not exist. Assume a, b , c, and k are fixed real numbers.

lim t→2+ |2t − 4|t^2 − 4

Find the following limits or state that they do not exist. Assume a, b , c, and k are fixed real numbers.

lim x→3 x − 3 /|x − 3|

Determine whether the following statements are true and give an explanation or counterexample. Assume a and L are finite numbers.

If limx→a f(x) = L, then f(a)=L.

Determine whether the following statements are true and give an explanation or counterexample. Assume a and L are finite numbers.

The limit lim x→a f(x) / g(x) does not exist if g(a)=0.

Evaluate lim x→2^+ √x−2.