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Simpsons Rule - PowerPoint PPT Presentation


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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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Presentation Transcript
slide1

Simpsons Rule

  • Formula given
  • Watch out for radians
  • Part b always linked to part a
slide2

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

slide3

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
slide4

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!

slide5

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
slide6

ExpDifferentiation and Integration

  • Power never changes
  • When differentiating, the power diffed comes down
  • When integrating, remember to take account of the above fact
slide7

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
slide8

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
slide9

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

slide10

Modulus Function

Get lxl =, then take + and - value

Solve 5x+7 between -4 and 4 as inequality

slide11

Inverse Functions

  • Write y=function
  • Rearrange to get x=
  • Rewrite inverse function in terms of x
slide12

Composite Functions

  • If ln and e function get them together to cancel out