What is the limit as x approaches 0 of (11sin(8x))/x ?

The limit as x approaches 0 of (11sin(8x))/x is 88

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limit as x approaches 0 of (11sin(8x))/x

x \to 0 lim (\frac{11 sin ( 8 x )}{x})

88

Solution steps

x \to 0 lim (\frac{11 sin ( 8 x )}{x})

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

= 11 \cdot x \to 0 lim (\frac{sin ( 8 x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( 8 x ) \cdot 8}{1})

= 11 \cdot x \to 0 lim (\frac{cos ( 8 x ) \cdot 8}{1})

Plug in the value

x = 0

= 11 \cdot \frac{cos ( 8 \cdot 0 ) \cdot 8}{1}

Simplify

11 \cdot \frac{cos ( 8 \cdot 0 ) \cdot 8}{1} : 88

= 88

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What is the limit as x approaches 0 of (11sin(8x))/x ?
The limit as x approaches 0 of (11sin(8x))/x is 88