SOLUTION: Prove the statement using the ε, δ definition of a limit. lim x^2=0 x→0 Given ε > 0, we need δ > 0 such that if 0 < |x − 0|

SOLUTION: Prove the statement using the ε, δ definition of a limit. lim x^2=0 x→0 Given ε > 0, we need δ > 0 such that if 0 < |x − 0| <  δ

Question 1046280: Prove the statement using the ε, δ definition of a limit.
lim x^2=0
x→0
Given ε > 0, we need δ > 0 such that if 0 < |x − 0| < δ, then |x2 − 0| < ε⇔ ____________ < ε ⇔
|x| < _____________. Take δ = ____________.Then 0 < |x − 0| < δ right double arrow implies
|x2 − 0| < ε. Thus,
lim
x→0 x^2 = 0 by the definition of a limit.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
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SOLUTION: Prove the statement using the &#949;, &#948; definition of a limit. lim x^2=0 x&#8594;0 Given &#949; > 0, we need &#948; > 0 such that if 0 < |x &#8722; 0| < &#8201;&#948;

SOLUTION: Prove the statement using the ε, δ definition of a limit. lim x^2=0 x→0 Given ε > 0, we need δ > 0 such that if 0 < |x − 0| < δ