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

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

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

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

- \frac{2}{π}

Decimal Notation

- 0.63661 \dots

Solution steps

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

Plug in the value

x = 0

= \frac{cos ( 0 )}{0 - \frac{π}{2}}

Simplify

\frac{cos ( 0 )}{0 - \frac{π}{2}} : - \frac{2}{π}

= - \frac{2}{π}

\int \frac{2 x ^{2}}{1 - 6 x ^{3}} d x

\frac{\partial}{\partial x} (sin (y) - y sin (x))

f (x) = 3 x^{3} - x^{2} + 2, (1, 4)

\int t^{3} \cdot ln (t^{2}) d t

\frac{\partial}{\partial y} (x y^{3} - x^{2})

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