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A math exam from koc university for the course math 102, held on april 24, 2012. The exam lasts 75 minutes and includes various calculus problems. Topics covered include limits, logarithmic functions, and finding extreme values and intercepts.
Typology: Exams
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SURNAME, Name: ————————————————–
Student ID no: —————————————————–
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(Check One):
(Selda K¨u¸c¨uk¸cif¸ci – MWF 9:30-10:20) : —– (Selda K¨u¸c¨uk¸cif¸ci – MWF 11:30-12:20) : —– (S¸ule Yazıcı – MWF 10:30-11:20) : —– (Ali G¨okt¨urk – MWF 12:30-13:20) : —– (Ali G¨okt¨urk – MWF 15:30-16:20) : —–
Problem 1. (25 pts) Calculate the following limits.
(a) lim x→ 0
sin x
x
(b) lim x→∞
x
(c) lim x→ 0
10 x^ − ex x − 1
(e) (9 pts) Find the inflection points and determine the intervals where the graph of the function f is concave up and concave down.
(f) (10 pts) Sketch the graph of the function f.
Problem 3. (15 pts) Find the absolute extremum of the function f (x) = 2x^3 − 9 x^2 + 1 on [-1,1].
Problem 4. (15 pts) The total cost of producing x garbage disposals per day is given by the function C(x) = 4000 + 10x + 0. 1 x^2
Find the minimum average cost.