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UPSC NDA Math Model Paper 5

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Comprehension:(Que No. 30 - 32)

Directions: For the next three (03) items that follow:Consider the function

f(x)=\begin{cases} x^{2}-5, & x \le 3 \\ \sqrt{x+13}, & x>3 \end{cases}

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Question : 30 of 120

Marks: +1, -0

What is

\lim\limits_{x\to 3}f(x)

equal to?

2
4
5
13

Solution:

Here,

\lim\limits_{x\to 3^{+}}f(x)=\lim\limits_{x\to 3^{+}}\sqrt{x+13}=4

And,

\lim\limits_{x\to 3^{-}}f(x)=\lim\limits_{x\to 3^{-}}x^{2}-5=4

So,

\lim\limits_{x\to 3}f(x)=4

Hence, option (2) is correct.

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