Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
main points of this exam paper are: Derivative to Compute, Function, Substituting Specific, Values, Rule, Interval, Increasing, Concave Down, Decreasing, Interval
Typology: Exams
1 / 9
This page cannot be seen from the preview
Don't miss anything!
Name:
Mathematics 105 Sections A, B, C, and D Final Exam Dec 15, 2009
Problem Possible Actual 1 10 2 20 3 10 4 20 5 10 6 15 7 24 8 15 9 20 10 20 11 18 12 18 Total 200
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.
f (x) =
− 1 x < 0 0 0 ≤ x < 2 1 2 ≤ x
Prove that f is not an even function by substituting specific values for x.
(a) On what interval is f ′^ increasing?
(b) On what interval is f concave down?
(c) On what interval is f decreasing?
(d) On what interval is f ′′^ increasing?
(e) On what interval is f ′^ concave down?
(a) lim x→ 0
2 − 2 cos x − x^2 x^4
(b) lim x→∞
sin x x
(c) lim x→ 0
x^3 − 1 7 − 7 x
dy dx
for the following expressions.
(a) y = 3x^ cos 5x
(b) y^4 + x^4 = 4x^2 y^2
(c) y = ex
(^2) sin x
(d) y =
∫ (^) x 2
6
arctan (ln t) dt
area of circle = πr^2 lateral area of cylinder = 2πrh volume of cylinder = πr^2 h”
(a) Draw a picture of what this problem describes, labeling any variables that you use.
(b) Write the constraint equation.
(c) Write the objective function.
