Math 242 - Calculus 1 - Sample Final
1) If f(x) = 3x+ 1 and g(x) = 4/(x+ 6), find formulas for the following and state the domains of the
functions.
a) (f+g)(2)
b) (f·g)(x)
c) (f◦g)(h)
2) Give an ε−δproof of the limit.
lim
x→3(4x−2) = 10
3) Find the limit.
lim
x→2
x3−8
x2−4
4) Find the limit.
lim
t→0
tan t
t
5) Use the limit definition of the derivative to find f′(x).
f(x) = x2+ 3x
6) Find dy/d x. Do not simplify your answer.
y=sin2(3x2+ 2x−4)
7) Find d2y/dx2. Do not simplify your answer.
y=x−2
3x2+ 2x1/2 −1
8) Find dy/d x. Do not simplify your answer.
y=tan3(x)x3+ 2
√
9) Find the maximum value and minimum value.
f(x) = x3−3x+ 1; x∈[−3,1]
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