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

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

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

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

k

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= k

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