Tuesday, November 18, 2014

Wednesday, November 12, 2014

One-sided limits from graphs

When approaching from the -ve side, there is a negative superscript for the limit number


    One-sided limits from graphs:




Monday, November 10, 2014

Function as geometric series

Find the common ratio r.

convergence occurs if  -1 < r < 1

For such an interval of convergence, S=a/(1-r)

  Function as geometric series:




Saturday, November 8, 2014

Tangent slope as limiting value of secant slope example 1

Draw out the graph to see what is needed.
It may be possible to substitute algebraically to get the solution.


    Tangent slope as limiting value of secant slope example 1:




Sunday, November 2, 2014

Relatively prime numbers

In number theory, two integers a and b are said to be relatively primemutually prime, or coprime (also spelled co-prime)[1] if the only positive integer that evenly divides both of them is 1. That is, the only common positive factor of the two numbers is 1. 

For example, 14 and 15 are coprime, being commonly divisible by only 1, but 14 and 21 are not, because they are both divisible by 7. 

Wednesday, October 29, 2014

Trapezoidal Rule to find the average value of f(x)

From http://www.intmath.com/integration/5-trapezoidal-rule.php

Area21(y0+y1)Δx+21(y1+y2)Δx+21(y2+y3)Δx+

AreaΔx(2y0+y1+y2+y3++2yn) for uniform grid


The trapezoidal rule finds the area. To get the average 
value, you will need to divide the area by b-a which is the
 the difference between the final and initial x values.

Friday, October 24, 2014

Inverse of a straight line

The straight line graphs shown below are inverses of one another.

 

Given the invertible function f(x), we determine the inverse by:
  • replacing every x with y and y with x;