What is the limit as x approaches 0 of ((cos(11x)-cos(6x)))/x ?

The limit as x approaches 0 of ((cos(11x)-cos(6x)))/x is 0

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limit as x approaches 0 of ((cos(11x)-cos(6x)))/x

x \to 0 lim (\frac{( cos ( 11 x ) - cos ( 6 x ) )}{x})

0

Solution steps

x \to 0 lim (\frac{cos ( 11 x ) - cos ( 6 x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{- 11 sin ( 11 x ) + 6 sin ( 6 x )}{1})

= x \to 0 lim (\frac{- 11 sin ( 11 x ) + 6 sin ( 6 x )}{1})

Plug in the value

x = 0

= \frac{- 11 sin ( 11 \cdot 0 ) + 6 sin ( 6 \cdot 0 )}{1}

Simplify

\frac{- 11 sin ( 11 \cdot 0 ) + 6 sin ( 6 \cdot 0 )}{1} : 0

= 0

f (x) = x^{3} sin (x)

\frac{d}{d x} (\frac{x ^{2} - 6 x + 1}{( x ^{2} - 1 ) ^{2}})

\int cos (x) (5 + 5 sin^{2} (x)) d x

\int x^{2} - 9 x + 3 d x

What is the limit as x approaches 0 of ((cos(11x)-cos(6x)))/x ?
The limit as x approaches 0 of ((cos(11x)-cos(6x)))/x is 0