Best solutions to - "Why does lim x → 0 + s..." - Plainmath

Agostarawz

Answered question

2022-07-02

Why does

lim_{x \to 0^{+}} s g n (x \sin^{2} (\frac{1}{x}))

not exist?

Answer & Explanation

Shawn Castaneda

Beginner2022-07-03Added 17 answers

The limit doe not exist, because

f (x_{n}) = 0

if

x_{n} = \frac{1}{n π}

and

f (x) = 1

if

x_{n} = \frac{1}{\frac{π}{2} + n π} (n \in N)

, and both sequences converge to 0

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