Page 10 - Calc for the Clueless

Same example, except x goes to minus infinity.

½
2
As x goes to plus or minus infinity, only the highest power of x counts. So (3x + 4 + 5) is approximately equal
½
to 3 |X| for very big and very small values of x.

Problems Involving

In proving that the derivative of the sine is the cosine, which is found in nearly every text, we also prove

This means if we take the sine of any angle and divide it by precisely the same angle, if we now take the limit
as we go to 0, the value is 1. For some reason, this topic, which requires almost no writing or calculation,
causes a tremendous amount of agony. Hopefully I can lessen the pain.

Fact 1

Fact 2

Fact 3

Example 15—

To use Fact I, since the angle on the top is 3x, the angle on the bottom must also be 3x. So put
the 4 on the left and multiply the bottom by the 3 you need. If you multiply the bottom by 3,
you must multiply the top by 3 so nothing changes.

Example 16—