In a study of towns there was a positive correlation between the number of mail boxes and number of traffic lights in a town. Wh
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We are given with a limit and we need to find it's value so let's start !!!!
But , before starting , let's recall an identity which is the <em>main key</em> to answer this question
Consider The limit ;
Now as directly putting the limit will lead to <em>indeterminate form 0/0.</em> So , <em>Rationalizing</em> the <em>numerator</em> i.e multiplying both numerator and denominator by the <em>conjugate of numerator </em>
Using the above algebraic identity ;
Now , here we <em>need</em> to <em>eliminate (√x-2)</em> from the denominator somehow , or the limit will again be <em>indeterminate </em>,so if you think <em>carefully</em> as <em>I thought</em> after <em>seeing the question</em> i.e what if we <em>add 4 and subtract 4</em> in <em>numerator</em> ? So let's try !
Now , using the same above identity ;
Now , take minus sign common in <em>numerator</em> from 2nd term , so that we can <em>take (√x-2) common</em> from both terms
Now , take<em> (√x-2) common</em> in numerator ;
Cancelling the <em>radical</em> that makes our <em>limit again and again</em> <em>indeterminate</em> ;
Now , <em>putting the limit ;</em>