Evaluate the limit, if it exists.

Question

lim , 3 − square root(x) /(9x − x^2)
x�¨9

Answer 1

When x = 9

9 x − x ^ 2 = 9 * 9 - 9 ^ 2 = 81 - 81 = 0

and

3 - sqt( x ) / ( 9 x − x ^ 2 ) =

3 - sqt( 9 ) / ( 9 x − x ^ 2 ) =

3 - 3 / 0 =

3 - ( + OR - infinity )

So:

limit 3 − square root( x ) /(9 x − x ^ 2 ) as x ->9 =

+ OR - infinity