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## Homework Statement

Find δ (which is the input tolerance):

lim (9 - 4x

^{2})/(3 + 2x

^{2}) = 6

x→-1.5

## Homework Equations

|f(x) - L| < [itex]\epsilon[/itex]

|x - a| < [itex]\delta[/itex]

## The Attempt at a Solution

lim (9 - 4x

^{2})/(3 + 2x

^{2}) = 6

x→-1.5

I need to get to:

|x-(-1.5)| < [itex]\delta[/itex]

=

|x + 1.5)| < [itex]\delta[/itex]

So:

|[(9 - 4x

^{2})/(3 + 2x

^{2})] - 6| < ε

|[(3 - 2x)(3 + 2x)/(3 + 2x)] - 6| < ε

|-2x - 3| < ε

|-2(x + 1.5)| < ε

|x + 1.5| < -ε/2

Therefore, δ = -ε/2

But when you divide an inequality equation by -2, aren't you supposed to switch the operator?

But the answer |x + 1.5| < -ε/2 = [itex]\delta[/itex] is what I wanted.

Thanks!

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