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Exam: NIMCET

NIMCETMathematics2010

If $f(x) = \begin{cases} x \sin\left(\frac{1}{x}\right) & \text{for } x \neq 0 \\ 0 & \text{for } x = 0 \end{cases}$ , then:

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NIMCETMathematics2019

Let f: R → R be defined by $f (x) = {x sin (\frac{1}{x}) 0 if x if x \leq 0 g t; 0$ Then

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NIMCETMathematics2021

If $f : R \to R$ is defined by:

$f (x) = ⎩ ⎨ ⎧ \frac{x + 2}{x ^{2} + 3 x + 2} - 1 0 if x \in R - {- 1, - 2} if x = - 2 if x = - 1$

Then, $f (x)$ is continuous on the set:

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NIMCETMathematics2022

The given function is defined as: $f (x) = {(1 + 2 x)^{\frac{1}{x}} e^{2} if x \neq = 0 if x = 0$

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NIMCETMathematics2024

Let $f (x) = {x^{2} sin \frac{1}{x}, 0, x \neq = 0 x = 0$

Then which of the following is true

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NIMCETMathematics2024

Let $f : R \to R$ be a function such that $f (0) = \frac{1}{π}$ and $f (x) = \frac{x}{e ^{π x} - 1}$ for $x \neq = 0$

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NIMCETMathematics2024

Consider the function

f(x) = \begin{cases} -x^3 + 3x^2 + 1, & \text{if } x \le 2, \\[4pt] \cos(x), & \text{if } 2 < x \le 4, \\[4pt] e^{-x}, & \text{if } x > 4. \end{cases}

Which of the following statements about $f(x)$ is true?

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