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

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

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

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

diverges

Solution steps

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

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

then the limit does not exist

x \to 1 + lim (\frac{cos ( x )}{x - 1}) = \infty

x \to 1 - lim (\frac{cos ( x )}{x - 1}) = - \infty

= diverges

x \to 2 lim (2 x^{3} - 5 x + 6)

x \to \infty lim (- \frac{x}{3})

x \to 4 + lim (\frac{8 - 2 x}{- 4 + x})

x \to - \infty lim (\frac{36 x ^{2} - 7 x}{4 - 3 x})

x \to 0 lim (x^{2^{- x}})

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