What is the limit as x approaches 0 of (cos(3x)tan(3x))/x ?

The limit as x approaches 0 of (cos(3x)tan(3x))/x is 3

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limit as x approaches 0 of (cos(3x)tan(3x))/x

x \to 0 lim (\frac{cos ( 3 x ) tan ( 3 x )}{x})

3

Solution steps

x \to 0 lim (\frac{cos ( 3 x ) tan ( 3 x )}{x})

cos (3 x) tan (3 x) = sin (3 x)

= x \to 0 lim (\frac{sin ( 3 x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( 3 x ) \cdot 3}{1})

= x \to 0 lim (\frac{cos ( 3 x ) \cdot 3}{1})

Plug in the value

x = 0

= \frac{cos ( 3 \cdot 0 ) \cdot 3}{1}

Simplify

\frac{cos ( 3 \cdot 0 ) \cdot 3}{1} : 3

= 3

y^{^{'}} = y - 2 x

\int \frac{4 x ^{3}}{1 + x ^{4}} d x

\frac{\partial}{\partial x} (x^{2} + 2)

\int_{1}^{8} \frac{5 ln ( x )}{x ^{2}} d x

n = 0 \sum \infty n - 2

What is the limit as x approaches 0 of (cos(3x)tan(3x))/x ?
The limit as x approaches 0 of (cos(3x)tan(3x))/x is 3