MATH 1131Q Study Guide - Final Guide: University Of Manchester, Riemann Sum, Thermostat
University of Connecticut
Department of Mathematics
Math 1131 Sample Final Exam Fall 2013
Name:
Instructor Name: Section:
TA Name: Discussion Section:
Read This First!
•Please read each question carefully. In order to receive full credit on a problem, solution
methods must be complete, logical and understandable.
•Answers must be clearly labeled in the spaces provided after each question. Please cross
out or fully erase any work that you do not want graded. The point value of each question is
indicated after its statement. No books or other references are permitted.
•Give any numerical answers in exact form, not as approximations. For example, one-third
is 1
3, not .33 or .33333. And one-half of πis 1
2π, not 1.57 or 1.57079.
•Turn smart phones, cell phones, and other electronic devices off (not just in sleep mode) and
store them away.
•Calculators are allowed but you must show all your work in order to receive credit on the
problem.
•If you finish early then you can hand in your exam early.
Grading - For Administrative Use Only
Question: 1 2 3 4 5 6 7 8 9 10 Total
Points: 15 8 12 12 8 8 10 9 10 8 100
Score:
4
Math 1131 Sample Final Exam
1. If the statement is always true, circle the printed capital T. If the statement is sometimes
false, circle the printed capital F. In each case, write a careful and clear justification or a
counterexample.
(a) [3]ln(23x) = 3 ln(2x). T F
Justification:
(b) [3]
d
dx(sin3x) = 3 sin2xcos xT F
Justification:
(c) [3]If f0(x) = ln xthen (f(x2))0= 4xln x. T F
Justification:
(d) [3]
Z2x
x2+ 1 dx = ln(x2+ 1) + C. T F
Justification:
(e) [3]If d
dx Z5
2
x2dx =x2. T F
Justification:
Page 1 of 10
Math 1131 Sample Final Exam
2. Use calculus to compute the following limits. If the limit does not exist, write DNE.
(a) [4]lim
x→2
4x−x4
x2−4
(b) [4]lim
x→∞
1000 ln x
x3
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MATH 1131Q Full Course Notes
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Document Summary
Read this first: please read each question carefully. In order to receive full credit on a problem, solution methods must be complete, logical and understandable: answers must be clearly labeled in the spaces provided after each question. Please cross out or fully erase any work that you do not want graded. The point value of each question is indicated after its statement. No books or other references are permitted: give any numerical answers in exact form, not as approximations. Justi cation: (b) d dx (sin3 x) = 3 sin2 x cos x. If f(cid:48)(x) = ln x then (f(x2))(cid:48) = 4x ln x. 2x x2 + 1 dx = ln(x2 + 1) + c. Sample final exam: use calculus to compute the following limits. If the limit does not exist, write dne. (a) lim x 2. 4x x4 x2 4 (b) lim x .
