What is the limit as x approaches 0 of (tan(4x))/(tan(9x)) ?

The limit as x approaches 0 of (tan(4x))/(tan(9x)) is 4/9

Popular >

limit as x approaches 0 of (tan(4x))/(tan(9x))

x \to 0 lim (\frac{tan ( 4 x )}{tan ( 9 x )})

\frac{4}{9}

Decimal Notation

0.44444 \dots

Solution steps

x \to 0 lim (\frac{tan ( 4 x )}{tan ( 9 x )})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{sec ^{2} ( 4 x ) \cdot 4}{sec ^{2} ( 9 x ) \cdot 9})

= x \to 0 lim (\frac{sec ^{2} ( 4 x ) \cdot 4}{sec ^{2} ( 9 x ) \cdot 9})

Plug in the value

x = 0

= \frac{sec ^{2} ( 4 \cdot 0 ) \cdot 4}{sec ^{2} ( 9 \cdot 0 ) \cdot 9}

Simplify

\frac{sec ^{2} ( 4 \cdot 0 ) \cdot 4}{sec ^{2} ( 9 \cdot 0 ) \cdot 9} : \frac{4}{9}

= \frac{4}{9}

x \to 1 lim (\frac{( x ^{7 a} - 7 a x + 7 a - 1 )}{( x - 1 ) ^{2}})

\int \frac{1}{( x + 8 ) ^{2}} d x

\frac{d}{d x} (- y ln (x) - (1 - y) ln (1 - x))

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

\frac{\partial}{\partial x} (sin (x t))

What is the limit as x approaches 0 of (tan(4x))/(tan(9x)) ?
The limit as x approaches 0 of (tan(4x))/(tan(9x)) is 4/9