What is the limit as x approaches 0 of [(sin(x))/x ] ?

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

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limit as x approaches 0 of [(sin(x))/x ]

x \to 0 lim ([\frac{sin ( x )}{x}])

1

Solution steps

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

\frac{d y}{d x} = y^{- 2}

y^{^{'''}} - 8 y^{^{''}} - 9 y^{^{'}} = 0

\int \frac{cos ^{2} ( θ )}{2} d θ

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

\int - 4 x sin (5 x) d x

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