MathematicsIf ⨍ (9)=9 and ⨍ ‘(9)=4, then limx→9⨍ (x)-3x-3 equals:

If $⨍ (9)=9$ and $⨍ '(9)=4,$ then $\lim_{x \to 9} \frac{\sqrt{⨍ (x)} - 3}{\sqrt{x} - 3}$ equals:

Solution:

The given limit is $\lim_{x \to 9} \frac{\sqrt{⨍ (x)} - 3}{\sqrt{x} - 3}$

Use LH rule

$\begin{array}{rcl} \lim_{x \to 9} \frac{\sqrt{⨍ (x)} - 3}{\sqrt{x} - 3} & = & \lim_{x \to 9} \frac{\frac{1}{2 \sqrt{⨍ (x)}} f' (x)}{\frac{1}{2 \sqrt{x}}} \\ = & \frac{1}{2 \sqrt{f (9)}} f' (9) \cdot 2 (3) \\ = & \frac{1}{2 (3)} 4 \cdot 6 \\ = & 4 \end{array}$

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