What is the limit as x approaches 0 of (cos(3x-pi/2))/x ?

The limit as x approaches 0 of (cos(3x-pi/2))/x is 3

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limit as x approaches 0 of (cos(3x-pi/2))/x

x \to 0 lim (\frac{cos ( 3 x - \frac{π}{2} )}{x})

3

Solution steps

x \to 0 lim (\frac{cos ( 3 x - \frac{π}{2} )}{x})

Join

3 x - \frac{π}{2} : \frac{6 x - π}{2}

= x \to 0 lim (\frac{cos ( \frac{6 x - π}{2} )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{- sin ( \frac{6 x - π}{2} ) \cdot 3}{1})

= x \to 0 lim (\frac{- sin ( \frac{6 x - π}{2} ) \cdot 3}{1})

Plug in the value

x = 0

= \frac{- sin ( \frac{6 \cdot 0 - π}{2} ) \cdot 3}{1}

Simplify

\frac{- sin ( \frac{6 \cdot 0 - π}{2} ) \cdot 3}{1} : 3

= 3

\frac{d}{d x} (ln (cot (5 x)))

f (x) = 4 x^{2} - 4 x + 1

y^{^{''}} + 2 y^{^{'}} + 2 y = sin (x)

\int \frac{1}{2 y - 1} d y

n = 0 \sum \infty 0. 9^{n}

What is the limit as x approaches 0 of (cos(3x-pi/2))/x ?
The limit as x approaches 0 of (cos(3x-pi/2))/x is 3