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 12 x^{2} ln (x) d x

arccot (15 y)

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

x^{2} y^{^{'}} + 2 x y = 13 cos^{2} (x)

y^{^{'}} + 3 x^{2} y = 6 x^{2}

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