What is the limit as x approaches 2 of (x-2)sin(1/(sqrt(x-2))) ?

The limit as x approaches 2 of (x-2)sin(1/(sqrt(x-2))) is Does not exist

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limit as x approaches 2 of (x-2)sin(1/(sqrt(x-2)))

x \to 2 lim ((x - 2) sin (\frac{1}{x - 2}))

Does not exist

Solution steps

x \to 2 lim ((x - 2) sin (\frac{1}{x - 2}))

x \to a - lim f (x) \neq = x \to a + lim f (x)

then the limit does not exist

x \to 2 + lim ((x - 2) sin (\frac{1}{x - 2})) = 0

x \to 2 - lim ((x - 2) sin (\frac{1}{x - 2})) =

Does not exist

= Does not exist

What is the limit as x approaches 2 of (x-2)sin(1/(sqrt(x-2))) ?
The limit as x approaches 2 of (x-2)sin(1/(sqrt(x-2))) is Does not exist