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H2 Math: GC Trick To Solve Maclaurin’s Series Problems Quickly!

Eg. Find the Maclaurin’s expansion for y = (sec x)^(1/2)

1. Select “y=” and Enter the equation above into “Y1”

2. Go to graph and find the value of y at x=0 by selecting “2nd” --> “trace” --> “value”

3. Under “Y2”, Enter “d/dx (Y2) | x=x”. (You can key in “Y2” by going to “vars” --> “Y-vars” --> "Function" --> “Y2”)

4. Repeat step 2 to find y at x=0.

5. Under “Y3”, Enter “d/dx (Y3) | x=x”

6. Repeat step 2 to find y at x=0

 

From the 2nd, 4th and 6th step respectively, you get y=1, y=0 and y=0.5 from your GC. Hence, your Maclaurin’s expansion is y = 1 + 1/4 x^2 + …

Note: you should only use this method to check your answers rather than solve them, otherwise you may not be awarded working marks in school. Cambridge, on the other hand, may give benefit of doubt.

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