Find the following limits or state that they do not exist. lim_{wrightarrow1}frac{acdot1}{(w^2-2)}-frac{1}{(w-1)b}

Maiclubk 2020-11-23 Answered
Find the following limits or state that they do not exist. limw1a1(w22)1(w1)b
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Expert Answer

Neelam Wainwright
Answered 2020-11-24 Author has 102 answers
Given,
limw1a1w221(w1)b
Rewrite the function:
lims11(as2sbs1)=lims11abss(s1)
The limit of product/quotient is the product/quotient of limits:
lims11abss(s1)=lims>11absslims>111s1
The limit of a quotient is the quotient of limits:
lims11(abs)slims111s1=lims111s1lims11abslims11s
Substitete the variable with the value:
lims111s1lims11(abs)lims>11s=lims111(s1)(ab)lims11s
Substitete the variable with the value:
(ab)lims111s1lims11s1=(ab)lims111s111
The function decreases without a bound:
lims111s1=
Therefore,
lims11as2sbs1=(ab)
Rewrite the function:
lims11as2sbs1=lims11abss(s1)
The limit of a product/quotient is the product/quotient of limits:
lims11abss(s1)=lims11absslims11(1s1)
The limit of quotient is the quotient of limits:
lims>111s1lims11abss=lims111s1lims11abslims11s
Substitute variable with the value:

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