- #1

Toshe

- 1

- 0

## Homework Statement

[itex]f(x,y) = 2x+3y[/itex]

Let [itex]\epsilon[/itex] be any positive number. Show that there is a disk with center [itex](1,1)[/itex] and radius [itex]\delta[/itex] such that whenever [itex]P[/itex] is in that disk, [itex]\left| f(P) - 5\right| < \epsilon[/itex]. Give [itex]\delta[/itex] as a function of [itex]\epsilon[/itex].

## Homework Equations

[itex]\left| 2x+3y - 5\right| < \epsilon[/itex]

[itex]\sqrt{(x-1)^2 + (y-1)^2} < \delta[/itex]

## The Attempt at a Solution

Obviously, it's a continuous equation that works out to exactly [itex]5[/itex] so the limit is 5. But I am stuck on solving for [itex]\delta[/itex] in terms of [itex]\epsilon[/itex]

I suspect I am stuck on an easy step.