Spring 2006

Justify all answers with neat and organized work. Clearly indicate your answers. 20 points possible.

1. (4 pts.) For the function g whose graph is given, state the value of each quantity, if it exists. If it does not exist, explain why.

(a) lim_{t® 2^-} g(t)

(b) lim_{t® 0⁺} g(t)

(c) g(2)

(d) lim_{t® 0} g(t)

2. (4 pts.) Determine the infinite limit.

lim x® 1  x-2 (x-1)2

3. (4 pts.) Evaluate the limit, if it exists. Your work must completely justify your answer algebraically.

lim x® -3  x2-9 x2+8x+15

4. (4 pts.) Evaluate the limit, if it exists. Your work must completely justify your answer algebraically.

lim x® 0    ___ Ö4+h   -2 h

5. (4 pts.) Explain why the function is discontinuous at the given number a. Sketch the graph of the function.

f(x)= x2+6x+16 x-2 if x ¹ 2

= -3 if x=2