Let , ,…

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let

f(x) = \begin{cases} x^n \sin\left(\frac{1}{x^2}\right), & x \neq 0 \\ 0, & x = 0 \end{cases}

,

(n \in \mathbb{I})

, then (1)

\lim_{x \to 0} f(x)

exists for every

n > 1

(2)

f

is continuous at

x = 0

for

n > 1

(3)

f

is differentiable at

x = 0

for every

n > 1

(4) None of the above

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