Quiz 5 Nov. 1, 2006

Calculus I Name:

Ver 1 Student ID:

Quiz 5

Nov. 1, 2006

1. (10 pts) Determine the value of a that makes the given function continuous (on (−∞, ∞)).

f (x) =

{ ae^x+ 1 if x < 0 x²+ x− 1 if x ≥ 0 Ans: a + 1 =−1 ⇒ a = −2

2. (10 pts) Determine the following limits (answer as appropriate, with a number, −∞,

∞ or does not exist).

•

limx→2

x² 4− x² lim

x→2⁻

x²

4− x² = +∞ (0 < x < 2; 4 − x² > 0)

xlim→2⁺

x²

4− x² =−∞ (x > 2; 4− x² < 0)

xlim→2

x²

4− x² DN E

•

xlim→∞

x²

4− x² = lim

x→∞

1

4/x²− 1 =−1

1