Question 123115


1)Find the value of lim(square root x)-(square root y)/x-a if lim x->a

lim<sub>x->a</sub>{{{(sqrt(x)-sqrt(a))/(x-a)}}}

Multiply by {{{(sqrt(x)+sqrt(a))/(sqrt(x)+sqrt(a))}}}

lim<sub>x->a</sub>{{{((sqrt(x)-sqrt(a)))/((x-a))}}}{{{((sqrt(x)+sqrt(a)))/((sqrt(x)+sqrt(a)))}}}

lim<sub>x->a</sub>{{{(  sqrt(x)sqrt(x)+sqrt(x)sqrt(a)-sqrt(a)sqrt(x)-sqrt(a)sqrt(a) )/

(  (x-a)(sqrt(x)+sqrt(a))   )}}}

lim<sub>x->a</sub>{{{(  x+sqrt(ax)-sqrt(ax)-a )/

(  (x-a)(sqrt(x)+sqrt(a))   )}}}

lim<sub>x->a</sub>{{{(  x-a )/

(  (x-a)(sqrt(x)+sqrt(a))   )}}}

lim<sub>x->a</sub>{{{cross(  x-a )/

(  cross(x-a)(sqrt(x)+sqrt(a))   )}}}

lim<sub>x->a</sub>{{{1/

(  (sqrt(x)+sqrt(a))   )}}}

{{{1/(sqrt(a)+sqrt(a))   }}}

{{{1/(2sqrt(a))   }}}

Edwin