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Calculus1

OpenStudy (anonymous):

Evaluate the given limit: lim x->3 ((x-3)/(sqrt(x) - sqrt(6-x))) (NO l'hospital)

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OpenStudy (gorv):

\[\frac{ x-3 }{ \sqrt{x}-\sqrt{6-x} }*\frac{ \sqrt{x} +\sqrt{6-x}}{ \sqrt{x}+\sqrt{6-x} }\]

OpenStudy (gorv):

(a-b)(a+b)=a^2-b^2

OpenStudy (gorv):

this will be applicable for denominator

OpenStudy (gorv):

\[\frac{ (x-3)(\sqrt{x}+\sqrt{6-x}) }{ (\sqrt{x})^2 -(\sqrt{6-x})^2}\]

OpenStudy (gorv):

\[\frac{ (x-3) *(\sqrt{x}+\sqrt{6-x}}{ x-6+x }\]

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OpenStudy (xapproachesinfinity):

no x isn't canceling in denominator we have 2x-6=2(x-3) cancel x-3 we are left with (root(x)+root(6-x))/2 now substitute directly the result is root(3)

OpenStudy (anonymous):

Oops, misread that as \(x-x\) for some reason... Thanks for pointing it out!

OpenStudy (xapproachesinfinity):

Welcome!^_^

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