I'm having trouble solving this limit: \(\displaystyle\lim_{{{x}\to-{2}^{{-}}}}{\frac{{{1}}}{{{\left({x}+{2}\right)}^{{2}}}}}\)

Malachi Mullins

Malachi Mullins

Answered question

2022-04-09

I'm having trouble solving this limit:
limx21(x+2)2

Answer & Explanation

cutimnm135imsa

cutimnm135imsa

Beginner2022-04-10Added 21 answers

Maybe this way of thinking about it will seem a little more intuitive to you:
Let ϵ>0, and consider the limit
limx21(x+2)2=limϵ01((2ϵ)+2)2
=limϵ01ϵ2
Now the expression 1ϵ2 can be made arbitrarily large by choosing ϵ small enough, and so the limit does not exist.
Jeffrey Jordon

Jeffrey Jordon

Expert2022-07-05Added 2605 answers

Answer is given below (on video)

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