Chapter 4, Problem 12PS

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Chapter
Section

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

# Proof(a) Prove that lim x → ∞ x 2 = ∞ (b) Prove that lim x → ∞ 1 x 2 = 0 (c) Let L be a real number. Prove that if lim x → ∞ f ( x ) = L , then lim y → ∞ + f ( 1 y ) = L

(a)

To determine

To prove: The limit limxx2= holds.

Explanation

Formula used:

The statement limxâ†’âˆžf(x)=a implies that for every Îµ>0 there would exist M>0 such that the following conditions holds whenever x>M:

|f(x)âˆ’a|<Îµ

Proof:

Let M>0

(b)

To determine

To prove: The limit limx1x2=0 holds.

(c)

To determine

To prove: If limxf(x)=L, then limy0+f(1y)=L.

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