Calculus

Introduction

This is my page on Calculus hopefully reminding me of my earlier youth

Limits

Intro

This is where you are given and equation and you have to specify the limit. The approach to solving these is

• Substitute the value asked for
• Multiply the top to cancel the bottom
• Multiply by the conjugate, this is where we take and expression with a real and imaginary part and flip the signs.So the x -3 has a real value of x and an imaginary value of -3.
  

We an multiply the top and the bottom by the conjugate

And then the answer is 1/6

Graphs

Limit on graph are simple, you take the measurement from the left, the measurement from the right and if they are the same you are good to go.

If they don't match then DNE (Does not exist) is the answer

Where the answer is infinity because the substitution is over 0. This produces the red line, a vertical asymptote. On the graph we can see at -3 on the x-axis the graph does not join up. This is a jump discontinuity and is not removable. At -2 we have hole which is a removable discontinuity.