What is the limit as x approaches 0 of (cos(2x)-cos(5x))/(x^2) ?

The limit as x approaches 0 of (cos(2x)-cos(5x))/(x^2) is 21/2

Popular >

limit as x approaches 0 of (cos(2x)-cos(5x))/(x^2)

x \to 0 lim (\frac{cos ( 2 x ) - cos ( 5 x )}{x ^{2}})

\frac{21}{2}

Decimal Notation

10.5

Solution steps

x \to 0 lim (\frac{cos ( 2 x ) - cos ( 5 x )}{x ^{2}})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{- 2 sin ( 2 x ) + 5 sin ( 5 x )}{2 x})

= x \to 0 lim (\frac{- 2 sin ( 2 x ) + 5 sin ( 5 x )}{2 x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{- 4 cos ( 2 x ) + 25 cos ( 5 x )}{2})

= x \to 0 lim (\frac{- 4 cos ( 2 x ) + 25 cos ( 5 x )}{2})

Plug in the value

x = 0

= \frac{- 4 cos ( 2 \cdot 0 ) + 25 cos ( 5 \cdot 0 )}{2}

- 4 cos (2 \cdot 0) + 25 cos (5 \cdot 0) = 21

= \frac{21}{2}

\int_{- 4}^{4} \frac{1}{2} (16 - x^{2}) d x

\int_{6}^{8} \frac{54}{( x - 6 ) ^{3}} d x

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

\int e^{5 x} cos (3 x) d x

\int cos (2 x) - sin (\frac{x}{2}) d x

What is the limit as x approaches 0 of (cos(2x)-cos(5x))/(x^2) ?
The limit as x approaches 0 of (cos(2x)-cos(5x))/(x^2) is 21/2