# MATH V1101 Study Guide - Midterm Guide: Farad, Even And Odd Functions, Constant Function

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School
Columbia University
Department
Mathematics
Course
MATH V1101
Professor Math 1101: Calculus I (Chao Li) Midterm I (Sample B)
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 For any function f(x), it is always true that lim
x!a
f(x)=f(a).
(2) T F The inverse function of f(x)=exis f1(x)=ex.
(3) T F cos(arccos(3
5)) = 4
5.
(4) T F Any one-to-one function passes the horizontal line test.
(5) T F lim
x!+1sin(x)=+.
(6) T F The derivative of the constant function f(x)=e5is f0(x)=e5.
(7) T F f(x)=1+ex
1exis an odd function.
(8) T F The equation ex=2+xhas a solution in the interval (0,2).
Problem 2. (5 points) The graph of y=f(x)=exis 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
6
8
10
12
(1) ←→ () y=2f(x)
(2) ←→ () y=f(x)
(3) ←→ () y=f(x)+6
(4) ←→ () y=f(2x+ 2)
(5) ←→ () y=f(2x3)
1
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