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Popular >

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

Solution

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

Solution

4

Solution steps

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 2 \cdot 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})

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

Plug in the value

x = 0

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

Simplify

2 \cdot \frac{cos ( 2 \cdot 0 ) \cdot 2}{1} : 4

= 4

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Frequently Asked Questions (FAQ)

What is the limit as x approaches 0 of (2sin(2x))/x ?
The limit as x approaches 0 of (2sin(2x))/x is 4