What is the limit as x approaches 0 of (1/x)tan(x) ?

The limit as x approaches 0 of (1/x)tan(x) is 1

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limit as x approaches 0 of (1/x)tan(x)

x \to 0 lim ((\frac{1}{x}) tan (x))

1

Solution steps

x \to 0 lim (\frac{1}{x} tan (x))

Simplify

\frac{1}{x} tan (x) : \frac{tan ( x )}{x}

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= 1

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

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

x \to 0 lim (\frac{x ( x + 1 )}{x})

x \to 0 lim (x e^{\frac{- 1}{x}})

x \to 1 lim (x^{2} - 5 x + 6)

What is the limit as x approaches 0 of (1/x)tan(x) ?
The limit as x approaches 0 of (1/x)tan(x) is 1