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UPSC NDA I 2021 Mathematics Solved Paper

Question : 94 of 120

Marks: +1, -0

What is

\lim\limits_{x \rightarrow 2}\;\frac{x^{3}+x^{2}}{x^{2}+3x+2}

Solution: 👈: Video Solution

Concept:

Continuity of a function:

- A function

f(x)

is said to be continuous at a point

x = a

in its domain, if

\lim\limits_{x \rightarrow a} f(x)

exists or if its graph is a single unbroken curve at that point.

f(x)

is continuous at

x = a \Leftrightarrow \lim\limits_{x \rightarrow a^{+}} f(x) = \lim\limits_{x \rightarrow a^{-}} f(x) = \lim\limits_{x \rightarrow a} f(x) = f(a)

Calculation:

\lim\limits_{x \rightarrow 2}\;\frac{x^{3}+x^{2}}{x^{2}+3x+2}

\;\; = \;\frac{2^{3}+2^{2}}{2^{2}+3\cdot2+2}

\;\; = \;\frac{12}{12}

\;\; = 1

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