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

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\int - \frac{1}{e ^{x}} d x

x \to - 2 lim (1 - x^{2})

\int \frac{x + 2}{x ^{2} + 16} d x

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