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

\int \frac{cos ( t )}{t} d t

\frac{d y}{d x} = x (y - 1)^{2}

y = (x^{3} - 16 x)^{10}, (4, 0)

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

\int_{0}^{5} e^{- 2 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