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Question

If $f left parenthesis 9 right parenthesis equals 9 comma f to the power of 1 left parenthesis 9 right parenthesis minus 4 comma$ then $L t divided by left parenthesis x rightwards arrow t right parenthesis space space left parenthesis √ left parenthesis f left parenthesis x right parenthesis right parenthesis minus 3 right parenthesis divided by left parenthesis √ x minus 3 right parenthesis$

1
4
0
3

hint Hint:

In this question we are getting $0 over 0$ form. So, we will use L'Hôpital's rule to find the limit.

The correct answer is: 4

In this question we are given $f left parenthesis 9 right parenthesis equals 9$ , $f apostrophe left parenthesis 9 right parenthesis equals 4$ and we have to find the limit of $limit as x minus greater than 9 of fraction numerator square root of f left parenthesis x right parenthesis end root minus 3 over denominator square root of x minus 3 end fraction$
Step1: Putting the value of limit
By putting the value of limits in the expression, we are getting both numerator and denominator as zero. That is $0 over 0$ form.
Step2: Using L'Hôpital's rule
In this rule we differentiate both numerator and denominator.
=> $limit as x minus greater than 9 of fraction numerator begin display style fraction numerator f apostrophe left parenthesis x right parenthesis over denominator 2 square root of f left parenthesis x right parenthesis end root end fraction end style over denominator begin display style fraction numerator 1 over denominator 2 square root of x end fraction end style end fraction$
By putting the value of limit we get,
$f apostrophe left parenthesis 9 right parenthesis equals 4$
Hence, the value of limit is $4$ .

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parallel

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parallel

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