Math 113 Exam #2 Solutions
1. An asteroid hits the Atlantic Ocean and creates an expanding circular wave. If the area enclosed by
this wave increases at the rate of 200 km2 /min, how fast is the diameter of the wave expanding when
its radius is 20 km?
Ans
Math 113 Exam #1 Practice Problems
1. Find the vertical asymptotes (if any) of the functions
g(x) = 1 +
2
,
x
h(x) =
4x
4 x2
What are the domains of g and h?
2. Evaluate
(a) lim
x2 x2
3. Evaluate
x2 4
5x + 6
|x + 2|
x2 x + 2
(b) lim
4x3 + 2x 4
x 4x2 5x +
Math 113 Exam #1 Practice Problems
1. Find the vertical asymptotes (if any) of the functions
g(x) = 1 +
2
,
x
h(x) =
4x
4 x2
What are the domains of g and h?
Answer: The function g has a vertical asymptote at x = 0. The function h has vertical asymptotes
Math 113 Exam #2 Practice Problem Solutions
f (x) and suppose f (3) = 1, f (3) = 8, and f (3) = 2. What is the value of u (3)?
1. Let u(x) =
Answer: Using the Chain Rule,
1
(f (x)1/2 f (x).
2
Hence, using the Chain Rule and the Product Rule,
u (x) =
u (x)
Math 113 Final Exam Practice Problems
1. What are the domain and range of the function
ln x
f (x) = ?
x
2. Find the inverse of the function f (x) = 1000(1 + 0.07)x .
3. Find the point on the graph of y = e3x at which the tangent line passes through the or
Math 113 Final Exam Practice Problem Solutions
1. What are the domain and range of the function
ln x
f (x) = ?
x
Answer: x is only dened for x 0, and ln x is only dened for x > 0. Hence, the domain of the
function is x > 0. Notice that
ln x
lim+ = ,
x
x0