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

The limit as x approaches 1 of sin(1/(x-1)) is diverges

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

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

diverges

Solution steps

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

Apply Limit Divergence Criterion:

diverges

= diverges

\int (x + x^{\frac{3}{4}}) d x

\frac{d}{d x} (4 x - 4 x)

\int \frac{x}{1 + 25 x ^{4}} d x

\int \frac{- 1}{x ^{2} x ^{2} - 9} d x

x \to \frac{π}{3} lim (sec (x))

What is the limit as x approaches 1 of sin(1/(x-1)) ?
The limit as x approaches 1 of sin(1/(x-1)) is diverges