Question 1:
Suppose f(x) = x2 – 2x + 3
Evaluate lim h → 0 [f(x + h) – f(x)]/h
Question 2:
Evaluate the following limits:
(a) lim x → ∞ (x2 + 3x)1/2 – x
(b) lim x → 3 (x3 – x + 26)/(x2 + 3)
Question 3:
Do the following limits exist? If so, evaluate them
(a) lim x → 0- 1/ |x|
(b) lim x → 3+ 1/| x - 3 |
Question 4:
(a) What is the domain of the following function?
f(x) = x/(x2 – 6x + 8)
(b) Suppose f(x) = 2x2 – 1
Find [f(x + 0.01) – f(x)]/0.01
Question 5:
Consider the following compound function h(x):
h(x) = x6 if x > 0
- x5 if x < 0
(a) Evaluate lim x → 0- h(x) and lim x → 0+ h(x)
(b) Does lim x → 0 h(x) exist? If so, find it
