# MATH V1101 Study Guide - Midterm Guide: Farad, 32X

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School
Columbia University
Department
Mathematics
Course
MATH V1101
Professor Math 1101: Calculus I (Chao Li) Midterm I (Sample A)
You have 75 minutes to complete your work. The total: 40 points.
Except for True/False and matching problems, show your reasons and computations.
No notes, books, calculators, computers, or other electronic aids are allowed.
Problem 1. (8 points) Mark True or False. No justiﬁcation is needed.
(1) T F The function tan(x) is continuous everywhere on the x-axis.
(2) T F Any function passes the horizontal line test.
(3) T F ln(ln e) = 0.
(4) T F The intermediate value theorem assures that a continuous function has a
derivative.
(5) T F arcsin(1
2) = 7π
4.
(6) T F The 100th derivative of the function f(x) = ex+x99 is f(100)(x) = ex.
(7) T F lim
x0sin( 1
x) = 0.
(8) T F f(x) = 12x
1 + 2xis an even function.
Problem 2. (4 points) The graph of y=f(x) = ln(x) is shown. Match the functions
(1) (5) on the left and curves (a)(e) on the right. No justication is needed.
y=f(x)
a
b
c
d
e
-2
-1
1
2
2
4
(1) ( ) y= 4f(x)
(2) ( ) y=f(x) + 1
(3) ( ) y=f(x)
(4) ( ) y=f(2x+ 2)
(5) ( ) y=f(2x3)
1
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