Math 170. Test 1
Summer 2009
June 25, 2009
1. Show the steps of your analysis in all answers: Unsubstantiated, incor-
rectly substantiated or illegible work does not qualify for credit.
2. Only work done in the blue books with your name on it will be considered
during the grading process.
Question 1
Given: f(x) = x2+ 3, a= 2 and L= 7. Find, for =1
4a positive value of δ
such that for each xwith 0 <|x−2|< δ, it is also true that |f(x)−7|< . (20
points)
Question 2
Use the tangent line method to approximate e0.1. (Hint: e0= 1.) (20 points)
Question 3
For f(x) = √3·x+ 1, use the definition of the derivative to compute the slope
of the the line tangent to the graph of fat the point (1,2). (15 points)
Question 4
For each of the following three functions, use the rules of differentiation and
knowledge of known derivatives to compute its derivative. Do this computation
one step at a time, indicating in each step which differentiation rules are used
in that step. (15 points each).
(a) f(x) = tan(x) + ln(arcsin(x)).
(b) f(x) = ln(x2)
ex.
(c) f(x) = x2·sec(arctan(x)).
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