Continuity

Intro

This is a question with 2 equations, it will help show if an equation is continous or not based on if all the values in the equation give us a real answer or not and how to find what kind of continuity without a graph

Sample Problem

1/X
3x/X
4/|x|+3

Solution

1/X is not continuous because when you use the table the first rule of continuity is not true. It gives you undefined when x = 0
So what kind of continuity is it? Plug in 0.00001 which gives you 10000 as an answer. So when X a proches 0 it goes up to infinity so infinite discontinuity.

Second one also has the same problem. It is discontinuous when X is 0 so we put X is equal to 0.00001 and it gives us 3. So it is removable.

Finally the last one is impossible to get 0 at the bottom which means that the function is continous throughout it’s whole domain.



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