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

y = \frac{25}{2} - \frac{x ^{2}}{2}, (- 5, 5)

\frac{d}{d x} (5 - 3 x)

20 t^{3}

y = sin^{2} (x^{2})

\frac{\partial}{\partial x} (ln (4 x^{2} + y^{2} + 2))

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