Use continuity to evaluate the limit \lim_{x\to4}\frac{12+\sqrt{x}}{\sqrt

Line 2021-10-21 Answered
Use continuity to evaluate the limit
limx412+x12+x
To find:
a) Domain of Numerator of function
b) Domain of denominator of the function
c) limit
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Expert Answer

liingliing8
Answered 2021-10-22 Author has 95 answers
a) Consider a given limit:
L=limx412+x12+x
Here
Numerator is 12+x and denominator =12+x
Now, find the domain of the numeratot.
Numerator 12+x is defined for all x[0,).
Hence domain of the numerator is [0,]
b) Now,
Denominator 12+x is not defined for all x=-12. Hence, the domain of the denominator 12+x is (12,).
Hence the domain of the function 12+x12+x is [0,)
c) Further, find the limit limx412+x12+x
Now,
L=limx412+x12+x
=12+412+4
=12+216
=144
=72
limx412+x12+x=72
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