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Simpsons Rule

Simpsons Rule. Formula given Watch out for radians Part b always linked to part a. Trig Equations. Use tan 2 x + 1 = sec 2 x Or 1 + cot 2 x = cosec 2 x Work through in sec x etc Convert to cos etc at end Bow ties to finish. Can’t change. Parametric Differentiation.

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Simpsons Rule

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  1. Simpsons Rule • Formula given • Watch out for radians • Part b always linked to part a

  2. Trig Equations • Use tan2x + 1 = sec2x • Or 1 + cot2x = cosec2x • Work through in sec x etc • Convert to cosetc at end • Bow ties to finish Can’t change

  3. Parametric Differentiation • x and y both in terms of another letter, in this case t • Work out dy/dt and dx/dt • dy/dx = dy/dt ÷ dx/dt • To get d2y/dx2 diff dy/dx again with respect to t, then divide by dx/dt

  4. Implicit Differentiation • Mixture of x and y • Diff everything with respect to x • Watch out for the product • Place dy/dx next to any y diff • Put dy/dx outside brackets • Remember that 13 diffs to 0 Product!

  5. Log Differentiation and Integration • Diff the function • Put the original function on the bottom • Bottom is power of 1 • Get top to be the bottom diffed

  6. ExpDifferentiation and Integration • Power never changes • When differentiating, the power diffed comes down • When integrating, remember to take account of the above fact

  7. Trig Differentiation and Integration • Angle part never changes • When differentiating, the angle diffed comes to the front • When integrating, remember to take account of the above fact • Radians mode

  8. Products and Quotient Differentiation • U and V • Quotient must be U on top, V on bottom • Product: V dU/dx + U dV/dx • Quotient: V dU/dx – U dV/dx • V2

  9. Iteration • Start with x0 • This creates x1etc • At the end, use the limits of the number to 4 dp to show that the function changes sign between these values Radians

  10. Modulus Function Get lxl =, then take + and - value Solve 5x+7 between -4 and 4 as inequality

  11. Inverse Functions • Write y=function • Rearrange to get x= • Rewrite inverse function in terms of x

  12. Composite Functions • If ln and e function get them together to cancel out

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