if a = 0 ; b = 0 ; then prove it a\b =2

Question

THINK OUTSIDE THE BOX

Answer 1

Let a=2b then a/b=2b/b=2. If a=2b=0 then a/b still equals 2 even though both a and b are zero and 0/0 would otherwise be undefined.

Comments

Thinking outside the box, if a=2b, then, when b=0, a is also zero. If we draw the graph of a=2b, where a is the vertical axis and b the horizontal axis, we have a straight line passing through the origin. The gradient or slope of the line is 2 at all points, including at the origin, where a=b=0. The gradient is a/b=2. Although strictly speaking a/b=0/0 which is undefined, we can choose b infinitesimally close to 0, so a=2b making a very close to zero, and the gradient remains at 2. So in the limit as b approaches zero, a/b=2.