Name:
Math 165: Calculus I Section M
Quiz #01
Question 1. Evaluate each limit:
y
y = f (x)
1
x
-1
1
2
-1
a) lim− f (x) =
x→0
b) lim− f (x) =
x→1
c) lim − f (x) =
x→−1
Question 2. Consider the function given by f (x) = x2 + x + 3. Evaluate
f (x + h) − f (x)
h→0
h
lim
Solution:
(x + h)2 + (x + h) + 3 − (x2 + x + 3)
h→0
h
2
2
x + 2xh + h + x + h + 3 − x2 − x − 3
= lim
h→0
h
2xh + h2 + h
= lim
h→0
h
h(2x + h + 1)
= lim
h→0
h
= lim 2x + h + 1 = 2x + 1
= lim
h→0
Page 2