Calculus I Name:
TA/classroom: Student ID:
Quiz 3
Oct. 24, 2007
1. (10 pts) Determine the value of a that makes the given function continuous at x = 0.
f (x) =
{ aex+ 2 if x < 0 a5x5+ a2x2+ x− a if x ≥ 0 Since
lim
x→0−f (x) = ae0+ 2 = a + 2, lim
x→0+f (x) =−a, f (0) =−a,
f (x) will be continuous at x = 0 if we let a + 2 =−a or a = −1.
2. Determine the following limits (answer as appropriate, with a number, −∞, ∞ or does not exist).
• (3 pts) lim
x→2−
x 2− x lim
x→2−
x
2− x = +∞ (x → 2− ⇒ 0 < x < 2; 2 − x > 0 and 2 − x → 0+)
• (3 pts) lim
x→2+
x 2− x lim
x→2+
x
2− x =−∞ (x → 2+ ⇒ x > 2; 2 − x < 0 and 2 − x → 0−)
• (4 pts) lim
x→+∞
x 2− x
xlim→∞
x
2− x = lim
x→∞
1
2/x− 1 =−1
