This problem can be solved using sandwitch theorem, We know that 1 ⇐ sin (1/x) ⇐ 1. Now multiply by x throughout x ⇐ x sin(1/x) ⇐ x. Now x approaches z ...

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Standard XII

Mathematics

Property 1

lim x → 0 x s...

Question

${lim}_{x \to 0} x s i n (\frac{1}{x})$

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Solution

This problem can be solved using sandwitch theorem,
We know that $- 1 \Leftarrow s i n (\frac{1}{x}) \Leftarrow 1.$
Now multiply by x throughout
$- x \Leftarrow x s i n (\frac{1}{x}) \Leftarrow x .$
Now x approaches zero, this inequality will look as below:
x $s i n (\frac{1}{x}) \Leftarrow 0.$
Hene the required limit is 0.

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{lim}_{x \to 0} x s i n (\frac{1}{x})

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limx→0xsin(1x)

This problem can be solved using sandwitch theorem, We know that −1 ⇐ sin (1x)⇐1. Now multiply by x throughout −x⇐x sin(1x)⇐x. Now x approaches zero, this inequality will look as below: x sin(1x)⇐0. Hene the required limit is 0.

${lim}_{x \to 0} x s i n (\frac{1}{x})$