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Math 171 Advanced Mathematics, Exercises of Mathematics

Fresno City CollegeMathematics

homework exercises for Math 171 at Fresno

Typology: Exercises

2019/2020

Uploaded on 03/12/2020

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PROBLEMS FOR LECTURE 25
Theorem 1.
The two statements below are equivalent
•limx→cf(x) = L
•
For any sequence
xn→c
,
xn6=c∀n
, it must be the case that
lim f(xn) = L
.
Problem 2.
Use the theorem above to prove that
lim
x→0sin 1
x
does not exists. Hint: Prove by contradiction: if the limit is some number
L
, then what happens?
Proof.
Insert proof here.
1

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PROBLEMS FOR LECTURE 25

Theorem 1. • limx→ (^) cThe two statements below are equivalent f (x) = L

Problem 2.^ •^ For any sequence Use the theorem above to prove that^ xn^ →^ c,^ xn^6 =^ c^ ∀n, it must be the case that^ lim^ f^ (xn) =^ L. does not exists. Hint: Prove by contradiction: if the limit is some number^ x^ lim→^0 sin^ x^1 L, then what happens? Proof. Insert proof here. 

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