1. Department of Computer Science
Midterm
April 7, 2015
5:00 pm to 6:30 pm
1. Evaluate the indicated limits.
(a) lim
x→−1
x + 1
x2 + 1
.
(b) Use the identity a3
− b3
= (a − b)(a2
+ ab + b2
) to evaluate lim
x→1
3
√
x − 1
x − 1
.
(c) limx→∞
x + 1
x2 + 1
.
(d) limx→∞
x2
− x4
.
2. Consider the function
f(x) =
x2
if x ≤ 0
2x if x > 0
(a) Is f continuous at x = 0? Justify.
(b) Is f differentiable at x = 0? Justify.
3. Find all asymptotes
f(x) =
x2
x + 4
4. Find the derivative of the following functions.
(a) f(x) = ln x2
(b) g(x) = sin2 x
3
5. Find the equation of the tangent line at the point (2, 1) for
x2
+ y3
− 2y − 3 = 0.
End