Question

limx->7 (2-(x-3)^(1/2))/(x^2-49)

Answer 1

(2-(x-3)^(1/2))/(x^2-49)

=((2-(x-3)^(1/2))*(2+(x-3)^(1/2)))/((x^2-49)*(2+(x-3)^(1/2)))

= (7-x)/((x-7)(x+7)((2+(x-3)^(1/2)))

= -1/((x+7)(2+(x-3)^(1/2))

=>

limx->7 (2-(x-3)^(1/2))/(x^2-49)

=

-1/((7+7)(2+(7-3)^(1/2))

=-1/56