What is the limit as x approaches 0 of (sin(5x))/x ?

The limit as x approaches 0 of (sin(5x))/x is 5

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limit as x approaches 0 of (sin(5x))/x

x \to 0 lim (\frac{sin ( 5 x )}{x})

5

Solution steps

x \to 0 lim (\frac{sin ( 5 x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( 5 x ) \cdot 5}{1})

= x \to 0 lim (\frac{cos ( 5 x ) \cdot 5}{1})

Plug in the value

x = 0

= \frac{cos ( 5 \cdot 0 ) \cdot 5}{1}

Simplify

\frac{cos ( 5 \cdot 0 ) \cdot 5}{1} : 5

= 5

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

\frac{d}{d x} (2 x sin (x) cos (x))

x \to 0 lim (\frac{1}{9 - 3 ^{\frac{1}{x}}})

cos (8 θ)

\int - \frac{1}{9} cos (3 x) d x

What is the limit as x approaches 0 of (sin(5x))/x ?
The limit as x approaches 0 of (sin(5x))/x is 5