cmi-entrance 2016 Q3

cmi-entrance · India · pgmath 4 marks Differentiating Transcendental Functions Regularity and smoothness of transcendental functions

Let $f : \mathbb{R} \longrightarrow \mathbb{R}$ be defined as $$f(x) = \begin{cases} x^2 \sin\left(\frac{1}{x^2}\right), & \text{if } x \neq 0 \\ 0, & \text{otherwise} \end{cases}$$ Choose the correct statement(s) from below:
(A) $f$ is continuous;
(B) $f$ is discontinuous at 0;
(C) $f$ is differentiable;
(D) $f$ is continuously differentiable.

Let $f : \mathbb{R} \longrightarrow \mathbb{R}$ be defined as
$$f(x) = \begin{cases} x^2 \sin\left(\frac{1}{x^2}\right), & \text{if } x \neq 0 \\ 0, & \text{otherwise} \end{cases}$$
Choose the correct statement(s) from below:\\
(A) $f$ is continuous;\\
(B) $f$ is discontinuous at 0;\\
(C) $f$ is differentiable;\\
(D) $f$ is continuously differentiable.

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17* Q18* Q19* Q20*