Holiday Reflection

Review blog
Whenever you are supposed to find a limit numerically, you use the table and if the numbers don’t match then the answer does not exist (DNE).
For Example:
Lim sin 2x/x
x>0
First you subtract or add 0 from -.1, -.01, -.001, .001, .01, and .1 to find the x-value.
Then you plug into your calculator for the y-value and should get 1.9867, 1.9999, 2, 2, 1.9999, and 1.986.
The means the limit is 2 because each side is approaching the same number.
Also, we learned how to plug in the number to find a limit.
For Example:
Lim x^4
x>-2
For this one you would plug in -2 for x, which would give you -2^4, so the answer would be 16.
Another Example:
Lim 2x-3/x+5
x>1
In this problem you plug in 1 for x, which would give you -1/6.

Also we learned derivatives.
There are quite a few different ways for the directions to tell you how to solve for a derivative. Those ways are:
y'
f'(x)
dy/dx
d/dx
Dx[y]
slope of a tangent line
slope of the curve at a point