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Material Type: Exam; Class: Calculus I; Subject: Mathematics; University: Boise State University; Term: Unknown 2009;
Typology: Exams
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Given: f(x) = x^2 + 3, a = 2 and L = 7. Find, for = 14 a positive value of δ such that for each x with 0 < |x − 2 | < δ, it is also true that |f(x) − 7 | < . ( points)
Use the tangent line method to approximate e^0.^1. (Hint: e^0 = 1.) (20 points)
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 f at the point (1, 2). (15 points)
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(x
(^2) ) ex^.
(c) f(x) = x^2 · sec(arctan(x)).