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Looking for Patterns in Calculus


Below is the formula for differentiating a fraction, using the Quotient Rule. Note that the ‘v‘s form a V on the outside of the formula, while the ‘u‘s are next to each other. D = Differential. This may help some senior students quickly learn the Quotient Rule (I tried this with a student some 30min after teaching it in class and they were able to write the formula accurately on the board). Sometimes it helps to use colour to show clear patterns in more complex formulae.

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10 x 9 x 8 + (7 + 6) x 5 x 4 x (3 + 2) x 1 = 2020

NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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