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Material Type: Exam; Professor: Moorhouse; Class: Calculus I; Subject: Mathematics; University: Colgate University; Term: Fall 2008;
Typology: Exams
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Math 111 – Calculus 1 Practice Problems for Exam 3 Fall 2008
(a) lim x→ 0 sin^ xx^3 −^ x (b) lim t→ 0 (sec x − tan x) (c) (^) xlim→∞ x^2 e−x (d) lim x→ 0 x^2 ln x^2
(e) (^) tlim→∞ t − ln t
(f) lim x→ 02
x (^) − 1 x (g) lim x→ 0 arcsinx^ x
(h) lim x→ 1 (ln^ x)
2 x
(a) Find the x and y intercepts of f. (b) Find the vertical and horizontal asymptotes of f. (c) Find the intervals on which f is increasing or decreasing. (d) Find all the points at which f has a local maximum or a local minimum. (e) Determine the intervals on which f is concave up or concave down, and find the inflection points. (f) Sketch the graph of f. Be sure to label all the x and y values of the intercepts, local maxima, local minima, inflection points, and asymptotes.
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