# Limit of cos x as x approaches 1 formal

## Homework Statement

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

## 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.

Mark44
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.

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