Find the limits: lim_{xrightarrow3}frac{-2}{x-3}

Tahmid Knox 2020-12-27 Answered
Find the limits:
limx32x3
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Expert Answer

Obiajulu
Answered 2020-12-28 Author has 98 answers
Given:
limx3(2x3)
LEFT-HAND LIMIT
Apply the constant multiple rule limx3cf(x)=climx3f(x) with c=2 and f(x)=1x3:
limx3(2x3)=(2limx31x3)
The function decreases without a bound:
limx31x3=
Therefore,
limx3(2x3)=
RIGHT-HAND LIMIT
Apply the constant multiple rule limx3+cf(x)=climx3+f(x) with c=2 and f(x)=1x3:
limx3+(2x3)=(2limx3+1x3)
The function grows without a bound:
limx3+1x3=
Therefore,
limx3+(2x3)=
Answer: limx3(2x3) does not exist, since the corresponding one-sided limits are not equal:
limx3(2x3)=, limx3+(2x3)=
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