What is the limit as x approaches 0 of sin(-1/x) ?

The limit as x approaches 0 of sin(-1/x) is diverges

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limit as x approaches 0 of sin(-1/x)

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

diverges

Solution steps

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

Simplify

sin (- \frac{1}{x}) : - sin (\frac{1}{x})

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

Apply Limit Divergence Criterion:

diverges

= diverges

f (x) = x^{3} - 3 x^{2} + 2

\frac{d y}{d t} = \frac{( t e ^{t} )}{y 5 + y ^{2}}

\frac{\partial}{\partial x} (c x)

f (x) = \frac{8}{x}, at x = 2

\int \frac{7 x ^{2} + 13 x}{x ^{3} + x ^{2} - x - 1} d x

What is the limit as x approaches 0 of sin(-1/x) ?
The limit as x approaches 0 of sin(-1/x) is diverges