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

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

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

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

1

Solution steps

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

Simplify

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

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

= \frac{cos ( 0 )}{1}

Simplify

\frac{cos ( 0 )}{1} : 1

= 1

x \to \infty lim (2^{x} - 4)

x \to 0 lim (1^{\frac{1}{x ^{2}}})

x \to 0 + lim (\frac{x + 1}{x})

y \to - 2 lim (g (y))

x \to 0 lim (e^{x} cos (4 x))

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