Question

Prove that if |x-x0| 13 years ago

Answer 1

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

Answer 2

then \[\left| xy-x0y0 \right|<ε\]

Answer 3

Hint: \[|xy-x_0y_0|=|xy-x_0y+x_0y-x_0y_0|\]

Answer 4

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

Answer 5

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

Answer 6

you'll want to apply the triangle equality first:\[|xy-x_0y+x_0y-x_0y_0|\le|xy-x_0y|+|x_0y-x_0y_0|\]Then factor and apply your hypothesis.

Answer 7

triangle inequality*

Answer 8

oh oh triangle inequality ahhhh never thought of that thxxx