Evaluate the following limits. lim_{(x,y)rightarrow(1,2)}frac{sqrt{y}-sqrt{x+1}}{y-x-1}

CoormaBak9 2021-01-13 Answered
Evaluate the following limits.
lim(x,y)(1,2)yx+1yx1
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Expert Answer

Clara Reese
Answered 2021-01-14 Author has 120 answers
We have to find the limit:
lim(x,y)(1,2)yx+1yx1
It is 00 form, since there is square root in numerator so applying rationalization rule multiplying and dividing by y+x+1,
lim(x,y)(1,2)yx+1(yx1)=lim(x,y)(1,2)(yx+1)(yx1)×(y+x+1)(y+x+1)
Since we know the identity, (ab)(a+b)=a2b2
Simplifying further,
lim(x,y)(1,2)(y)2(x+1)2(yx1)(y+x+1)=lim(x,y)(1,2)y(x+1)(yx1)(y+x+1)
=lim(x,y)(1,2)(yx1)(yx1)(yx+1)
=lim(x,y)(1,2)1(y+x+1)
=1(2+1+1)
=1(2+2)
=122
Hence, value of limits is 122
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Jeffrey Jordon
Answered 2022-04-01 Author has 2047 answers

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