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A mathematics exam from a university-level course, mathematics 105. The exam covers various topics including calculus, limits, derivatives, and concavity. Students are required to find exact answers and show all work to receive credit. The exam includes problems related to finding inflection points, evaluating limits, and estimating derivatives.
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Mathematics 105 Exam I October 9, 2009
Problem Possible Actual 1 15 2 15 3 15 4 20 5 20 6 15 Total 100
You must show all work to receive credit. No electronic devices other than calculators are permitted. Give exact answers (such as ln 5 or e^2 ) unless requested otherwise.
(a) Explain why f (x) has only one inflection point.
(b) Find f (x) if f ′(0) = 1 and f (1) = 0.
(a) lim x→ 0
x x
(b) lim x→ 0
|x| x
(c) lim h→ 0
(2 + h)^6 − 26 h
(d) lim x→ 4
x − 2 x − 4
