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

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

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

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

3

Solution steps

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 3 \cdot x \to \frac{π}{2} lim (\frac{cos ^{2} ( x )}{2 - 2 sin ( x )})

Apply L'Hopital's Rule

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

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

Simplify

\frac{- sin ( 2 x )}{- 2 cos ( x )} : sin (x)

= 3 \cdot x \to \frac{π}{2} lim (sin (x))

Plug in the value

x = \frac{π}{2}

= 3 sin (\frac{π}{2})

Simplify

3 sin (\frac{π}{2}) : 3

= 3

x \to \frac{π}{3} lim (\frac{1 - 2 cos ( x )}{π - 3 x})

x \to - 2 lim (3 x - 2)

x \to 0 lim ((csc (x))^{x})

x \to 0 lim (x^{3} + 3 x^{2} - x + 1)

x \to \infty lim (x - 3 x^{2})

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