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

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

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limit as x approaches+0 of (tan(8x))/x

x \to + 0 lim (\frac{tan ( 8 x )}{x})

8

Solution steps

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{sec ^{2} ( 8 x ) \cdot 8}{1})

= x \to 0 lim (\frac{sec ^{2} ( 8 x ) \cdot 8}{1})

Plug in the value

x = 0

= \frac{sec ^{2} ( 8 \cdot 0 ) \cdot 8}{1}

Simplify

\frac{sec ^{2} ( 8 \cdot 0 ) \cdot 8}{1} : 8

= 8

x \to 8 lim (2 x - 8)

x \to 0 lim (2 \frac{tan ^{2} ( x )}{x})

x \to - 2 lim (5 x^{3} + 3 x^{2} - 6)

x \to 0 lim (\frac{3 ^{x} - 5 ^{x}}{x})

x \to 2 lim (2 x^{2} - 4 x + 8)

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