What is the limit as (x,y) approaches (pi, pi/2) of ysin(x-y) ?

The limit as (x,y) approaches (pi, pi/2) of ysin(x-y) is pi/2

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limit as (x,y) approaches (pi, pi/2) of ysin(x-y)

(x, y) \to (π, \frac{π}{2}) lim (y sin (x - y))

\frac{π}{2}

Decimal

1.57079 \dots

Solution steps

(x, y) \to (π, \frac{π}{2}) lim (y sin (x - y))

Plug in the value

(x, y) = (π, \frac{π}{2})

= \frac{π}{2} sin (π - \frac{π}{2})

Simplify

\frac{π}{2} sin (π - \frac{π}{2}) : \frac{π}{2}

= \frac{π}{2}

What is the limit as (x,y) approaches (pi, pi/2) of ysin(x-y) ?
The limit as (x,y) approaches (pi, pi/2) of ysin(x-y) is pi/2