Limit of cos x as x approaches 1 formal

1. Sep 16, 2009

enkerecz

1. The problem statement, all variables and given/known data

The limit of Cos X as x approaches one using the formal definition.
Given epsilon values of .1, .001, .00001

2. Relevant equations

3. The attempt at a solution

Spent all period in physics calc trying to solve this using the formal definition.
Since there is no way to manipulate abs(cosx-.5403)<epsilon
I proceeded to make my delta = the epsilon values and plug into the equation.
None of the answers were working correctly. Any help would be greatly appreciated because i have a feeling that im missing something here.

2. Sep 16, 2009

Staff: Mentor

It appears you want to find the individual values of delta when epsilon is .1, .001, and .00001.

Set up your inequality for each of these values.
For epsilon = .1

|cos x - 0.5403023| < .1
<==> -.1 < cos x - 0.5403023 < .1
Continue in this vein until you have cos x between two values, and then use cos-1 to get an inequality in x. At that point you should have a good idea what to use for delta.

Do the same for the other two values of epsilon.

3. Sep 16, 2009

LCKurtz

Hint: You might find this identity useful:

$$\cos{a} - \cos{b} = -2 \sin \frac {a+b} 2 \sin \frac {a-b} 2$$