InterviewSolution
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InterviewSolution
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Evaluate `lim_(x rarr 3) ((3 - sqrt(6+x)))/(x-3)`. |
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Answer» When `x=3, ((3-sqrt(6+3)))/(3-3)=(0)/(0)`, which is an indeterminate form. As f(x) is irrational, we multiply the numerator and denominator with the rationalizing factor of f(x). `underset(x rarr 3)("lim")((3-sqrt(6+x)))/(x-3)=underset(x rarr 3)("lim")((3-sqrt(6+x)))/(x-3)xx((3+sqrt(6+x)))/((3+sqrt(6+x)))=underset(x rarr 3)("lim")(9-(6+x))/((x-3)(3+sqrt(6+x)))` `" "underset(x rarr 3)("lim")(3-x)/((x-3)(3+sqrt(6+x)))=underset(x rarr 3)("lim")(-1)/((3+sqrt(6+x)))=(-1)/((3+sqrt(6+3)))` `" "underset(x rarr 3)("lim")(-1)/((3+3))=-(1)/(6)`. |
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