Find the value limx→4(√(x−3−1)/x−4)

babeeb0oL

babeeb0oL

Answered question

2021-02-15

Find the value limx4(x31x4)

Answer & Explanation

l1koV

l1koV

Skilled2021-02-16Added 100 answers

We have to find
limx4((x3)1x4)
Note that we can not find the value of limit by plugging x=4, as in that case the denominator become zero. Let us first rationalize numerator.
(x3)1x4=(x3)1(x3)+1x4×x3+1

=((x3)2)12(x4)(x3+1=x4(x4)(x3+1=1x3+1
Therefore we have limx4(x3)1x4=limx4(x3)1x4=limx4(1x31)=143+1=12

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