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.

i have reached my limit...

what i dont get about limits

-one thing i don't get about limits is when to plug it it. because occasionally you have to solve first then you can plug it in. what makes it right to solve first then plug it in until it cannot simplify any longer???

ex: lim 1/2+x-1/2/x

x-->

to solve first you ave to find the least common demonator for the fractioned numerator but why cant you just

what i do get.

2. the limit of a constant will always give you that constant as the answer.

3. you can occasionally brake limits apart. that can make it easier because you ccan then find the limit for the separate equations.