Q.Find the value of $\lim\limits_{x \to 5} \dfrac{x^2 - 25}{x - 5}$

Substitute $x=3$ directly: the limit equals $3$.

Since the denominator $x+3\neq 0$ at $x=3$, the expression is continuous there and we substitute directly: …

Direct substitution gives $\lim\limits_{x\to 3}(x^2+3)=12$.

$x^2+3$ is a polynomial, hence continuous at every point, so the limit equals the function value …

The limit is $2$.

Since the denominator $x+2$ is non-zero at $x = 2$, the function is continuous there and the limit is found by direct substitution: …

Correct option: (a) 4.

At $x = 2$ the expression is $\dfrac{0}{0}$ (indeterminate), so factorise the numerator as a difference of squares: …