Practice Book for KVPY Aptitude Test - Stream SX Mathematics>Chapter 5 - Continuity & Derivability>EXERCISE>Q 17

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Let $y = f (x) = \{\begin{array}{cl} e^{- \frac{1}{x^{2}}} & if x \neq 0 \\ 0 & if x = 0 \end{array}$ . Then which of the following can best represent the graph of $y = f (x)$ ?

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Important Questions on Continuity & Derivability

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Practice Book for KVPY Aptitude Test - Stream SX Mathematics>Chapter 5 - Continuity & Derivability>EXERCISE>Q 18

If

f (2 + x) = f (- x)

for all

x \in R,

then differentiability at

x = 4

implies differentiability at

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Practice Book for KVPY Aptitude Test - Stream SX Mathematics>Chapter 5 - Continuity & Derivability>EXERCISE>Q 19

If both

f (x)

and

g (x)

are differentiable functions at

x = x_{0}

, then the function defined as

h (x) =

maximum

\{f (x), g (x)\}

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Practice Book for KVPY Aptitude Test - Stream SX Mathematics>Chapter 5 - Continuity & Derivability>EXERCISE>Q 20

Let

f (x) = \lim_{n \to \infty} \frac{{(x^{2} + 2 x + 3 + \sin π x)}^{n} - 1}{{(x^{2} + 2 x + 3 + \sin π x)}^{n} + 1}

, then