What is the value of _ x 3 x^2-9 x-3 - Vidyadip

MCQ

What is the value of $\lim_{\text{x} \rightarrow 3}\frac{\text{x}^2-9}{\text{x}-3}$

A
$0$
B
$3$
C
Infinity
✓
$6$

✓

Answer

Correct option: D.

$6$

When $x$ tends to $3,$ both the numerator and,
the denominator become $0$ and it becomes of the form, $0$.
Therefore, we use $L’$Hospital’s rule,
which states the we differentiate the numerator and the denominator,
until a definite answer is reached.
On differentiating once we get,
$\lim_{\text{x} \rightarrow 3}\frac{2\text{x}}{1}$
Since, this not an indeterminate form now, we can substitute the value of $x.$
$= 2 \times 3$
$= 6$

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