The value of $\lim_{x \to 3} \frac{x^2+9}{x+3}$ is : (a) 1 (b) 2 (c) 3 (d) 4

The value of limx → 3 (x²+9)/(x+3) is : (a) 1 (b) 2 (c) 3 (d) 4

CBSE 2024Set ANNUAL1 markMCQ

\lim_{x \to 3} \frac{x^2+9}{x+3}

(a) 1

(b) 2

(c) 3

(d) 4

›Reveal solution

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: …

CBSE 2023Set ANNUAL1 mark

\lim\limits_{x \to 3}(x^2 + 3)

›Reveal solution

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 …

CBSE 2019Set ANNUAL1 mark

Q. Answer each of the following questions in one sentence:

(x) Evaluate:

\lim\limits_{x \to 2} \dfrac{x^2 + 4}{x + 2}

.

›Reveal solution

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: …

CBSE 2019Set ANNUAL1 markMCQ

\lim\limits_{x \to 2} \dfrac{x^2 - 4}{x - 2}

(a)

4

(b)

2

(c)

0

(d)

\infty

›Reveal solution

Correct option: (a) 4.

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