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

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

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

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

1

Solution steps

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

Simplify

sin (x) \frac{1}{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

\frac{d}{d x} ((\frac{2 x}{x + 2})^{4})

x \to 8 lim (\frac{( x + 6 )}{x - 8})

\int \frac{x ^{2}}{( 5 + x ^{3} ) ^{2}} d x

f (x) = - 2 cos (x)

\int x - \frac{2}{x} d x

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