What is the limit as x approaches 0 of ((sin(2x)))/x ?

The limit as x approaches 0 of ((sin(2x)))/x is 2

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limit as x approaches 0 of ((sin(2x)))/x

x \to 0 lim (\frac{( sin ( 2 x ) )}{x})

2

Solution steps

x \to 0 lim (\frac{sin ( 2 x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( 2 x ) \cdot 2}{1})

= x \to 0 lim (\frac{cos ( 2 x ) \cdot 2}{1})

Plug in the value

x = 0

= \frac{cos ( 2 \cdot 0 ) \cdot 2}{1}

Simplify

\frac{cos ( 2 \cdot 0 ) \cdot 2}{1} : 2

= 2

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

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

y = x sin (x) + cot (x)

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

z^{3} - 5 z + 4

What is the limit as x approaches 0 of ((sin(2x)))/x ?
The limit as x approaches 0 of ((sin(2x)))/x is 2