What is the limit as x approaches 0 of ((sin(4x)))/x ?

The limit as x approaches 0 of ((sin(4x)))/x is 4

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limit as x approaches 0 of ((sin(4x)))/x

x \to 0 lim (\frac{( sin ( 4 x ) )}{x})

4

Solution steps

x \to 0 lim (\frac{sin ( 4 x )}{x})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{cos ( 4 x ) \cdot 4}{1})

Plug in the value

x = 0

= \frac{cos ( 4 \cdot 0 ) \cdot 4}{1}

Simplify

\frac{cos ( 4 \cdot 0 ) \cdot 4}{1} : 4

= 4

x \to 0 lim (5 x)

t an g e n t f (x) = \frac{- 5}{x - 1}, at a = 8

t an g e n t r = 1 + cos (θ)

d er i v a t i v e g (x) = (2 x^{2} + x + 9)^{- 3}

\frac{d}{d y} (e^{3 x} (3 x^{2} y + 2 x y + y^{3}))

What is the limit as x approaches 0 of ((sin(4x)))/x ?
The limit as x approaches 0 of ((sin(4x)))/x is 4