Prove that if |x-x0|

Question

Prove that if |x-x0|<min(ε/2(|y0|+1),1) and |y-y0|<ε/2(|x0|+1) then |xy-x0y0|<ε .
If it's possible i want a hint and not the full solution

anonymous · Answer

$$\left| x-x0 \right|<\min(\frac{ ε }{ 2(|y0|+1)},1)$$
$$\left| y-y0 \right|<\frac{ ε }{ 2(|x0|+1) }$$

anonymous · Answer

then $$\left| xy-x0y0 \right|<ε$$

anonymous · Answer

Hint: $$|xy-x_0y_0|=|xy-x_0y+x_0y-x_0y_0|$$

anonymous · Answer

|y(x-x0) + x0(y-y0)|<ε     it goes like that next right?

anonymous · Answer

ive reached that...the point is i dont know what to do after that..

anonymous · Answer

anonymous · Answer

triangle inequality*

anonymous · Answer

oh oh triangle inequality ahhhh never thought of that thxxx