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
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-> 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
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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):
