Correct Answer - Option 2 : 1
Concept:
Continuity of a function:
- A function f(x) is said to be continuous at a point x = a in its domain, if \(\rm \lim_{x\to a}f(x)\) exists or if its graph is a single unbroken curve at that point.
- f(x) is continuous at x = a ⇔ \(\rm \lim_{x\to a^+}f(x)=\lim_{x\to a^-}f(x)=\lim_{x\to a}f(x)=f(a)\).
Calculation:
\(\rm \lim_{x \to 2} \frac{x^3 + x^2}{x^2 + 3x + 2}\)
= \(\rm \frac{2^3 + 2^2}{2^2 + 3\cdot2 + 2}\)
= \(\frac{12}{12}\)
= 1.
