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

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

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

x \to 0 lim (\frac{sin ( 2 \cdot 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

t \to 0 + lim ((t - 2)^{5})

x \to 0 lim (x - sin (2 x))

x \to 0 lim (39 - x^{22} x + 1)

n \to \infty lim (- 5^{n})

x \to 2 lim (\frac{f ( x )}{x})

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