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UPSC NDA I 2016 Mathematics Solved Paper

Question : 82 of 120

Marks: +1, -0

What is

\underset{x→0}{lim} e^{-\frac{1}{x^{2}}}

equal to?

Solution:

Concept:

The limit involves an exponential function where the exponent tends to

-\infty

, making the whole expression approach

0

Explanation:

Consider

\underset{x \to 0}{\lim} e^{-\frac{1}{x^{2}}}

x \to 0

, the term

\frac{1}{x^{2}} \to +\infty

Therefore,

-\frac{1}{x^{2}} \to -\infty

The exponential function

e^{t}

tends to

0

when

t \to -\infty

Thus, the limit simplifies to

e^{-\infty} = 0

Answer:

The limit equals

0

Correct option: A.

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