Find the limits: lim_{xrightarrow4}frac{4x-x^2}{2-sqrt{x}}

geduiwelh 2020-12-16 Answered
Find the limits: limx44xx22x
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Expert Answer

estenutC
Answered 2020-12-17 Author has 81 answers
We have to find the limits:
limx44xx22x
It is 00 form
Simplifying the limit by using rationalization of denominator.
Multiplying and dividing by (2+x),
limx44xx22x×(2+x)(2+x)
We know the idenity,
(ab)(a+b)=a2b2
Therefore,
limx44xx22x×(2+x)(2+x)=limx4(4xx2)(2+x)(2)2(x)2
limx4x(4x)(2+x)4x (taken x common from 4xx2)
limx4x(2+x)
=4(2+4)
=4(2+2)
=4×4
=16
Hence, value of limit is 16.
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Jeffrey Jordon
Answered 2022-04-01 Author has 2087 answers

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