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

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

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

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

8

Solution steps

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

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

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= 8

x \to 1 + lim (\frac{x ^{3}}{x ^{2} - 1})

x \to \frac{1}{2} lim (12 + x - x^{2})

x \to 4 + lim (\frac{x}{( x - 4 ) ^{2}})

x \to 0 + lim (- 1 + ln (x) x)

x \to 0 lim (sin (x) cot (x))

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