Algebra vs Calculus

Finding the limit of a constant and the output of a constant.

• Fnding the limit of f(x) as x->c could have two different ouputs.

For exapmle: the function f(x)=x/absolute value x the limits as x->0+ side equals 1.

and as the limit as x->0- equals -1. however

• Plugging in the constant will only give you one output.

When just plugging the number 0 it gives you only one output. In this case however there is no output for f(0).

• These two cases could be the same when the limit as x approaches the constant and when just plugging in the constant are equal.

For example: the function f(x)= x^2

The limit as any constant from both the positive side will give you one output.this goes with plugging in the constant too because it gives you the same output.

basically: limit x->c+ f(x)=limit x->c- f(x)=f(c)

Difference between slope of the line and the derivitave.

• The slope of the line.

The slope of line only determines the slope for that single point.

• Derivitave

The derivitave gives you the formula to find the slope for function to every direction of the function so the function must be continuous.

• They are similiar because the give the dx/dy for the given point.