Simpsons Rule

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# Simpsons Rule - PowerPoint PPT Presentation

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

Simpsons Rule

• Formula given
• Part b always linked to part a

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

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

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!

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

ExpDifferentiation and Integration

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

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

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

Iteration

• 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

Modulus Function

Get lxl =, then take + and - value

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

Inverse Functions

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

Composite Functions

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