What is the limit as x approaches 0 of (tan(5x))/x ?

The limit as x approaches 0 of (tan(5x))/x is 5

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limit as x approaches 0 of (tan(5x))/x

x \to 0 lim (\frac{tan ( 5 x )}{x})

5

Solution steps

x \to 0 lim (\frac{tan ( 5 x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{sec ^{2} ( 5 x ) \cdot 5}{1})

= x \to 0 lim (\frac{sec ^{2} ( 5 x ) \cdot 5}{1})

Plug in the value

x = 0

= \frac{sec ^{2} ( 5 \cdot 0 ) \cdot 5}{1}

Simplify

\frac{sec ^{2} ( 5 \cdot 0 ) \cdot 5}{1} : 5

= 5

\int \frac{1}{x ^{3}} - x d x

\frac{d}{d x} (x^{3} (x - 3)^{2})

x \to 0 lim (2)

\frac{d}{d x} (\frac{1}{3} x^{3} + 2 x - 4)

n = 0 \sum \infty (\frac{6}{5})^{n}

What is the limit as x approaches 0 of (tan(5x))/x ?
The limit as x approaches 0 of (tan(5x))/x is 5