1 / 9

Maths Aim Higher

Maths Aim Higher. Calculus of Small increments. A first principles approach. In general, the derivative f ’ (x) evaluated at x = a can be defined as Click here to see how this works with quadratics. Practice makes perfect !. Click here to practice first principles on quadratics

menefer
Download Presentation

Maths Aim Higher

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Maths Aim Higher Calculus of Small increments

  2. A first principles approach In general, the derivative f ’ (x) evaluated at x = a can be defined as Click here to see how this works with quadratics

  3. Practice makes perfect ! Click here to practice first principles on quadratics Click here for first principles applied to rational expressions Click here to apply first principles to surdal expressions Click here for a check test on first principles

  4. Setting up a formula Another way to express this is …. If P ( x, y ) is a point on the curve y = f (x) and Q (x + , y + ) is close to P. Then is a small increase in x , and is the corresponding increase in y.

  5. The formula is established Now, by definition. So when is small, Hence, We can now investigate changes affecting other variables

  6. Example: y = ln x We know that Hence When x = 1, y = ln 1 = 0 Taking (small) and Then ln 1.1 = = 0 + 0.1 = 0.1 So ln 1.1 0.1

  7. Percentage increments If x increases by r% then Hence, corresponding % increase in y is given by Let’s see an example in action ……..

  8. The pendulum problem Given Find % change in T when l is increased by 2% Well, So Given And so …………

  9. Pendulum problem (ctd) Since Then So % change in T = So period T increases by 1%

More Related