Using GC to check Maclaurin's Series

For Maclaurin's series, much of the solution is theoretical, involving repeated differentiation (often implicit) and hence, the GC is only used, for example, to compute the value of the derivatives in the 2nd step of the Maclaurin procedure.

While GC can't be used to help solve a Maclaurin question, it can be used to check our answers.
To check the final answer, enter Y1 = original function and Y2 = Maclaurin expansion that we found. If both graphs agree consistently for much of the region near the origin, then very likely, you have got it right!

GC can also be used to check individual values for the 2nd step of the Maclaurin procedure (hence, verifying that differentiation had been correctly done).
Enter Y1 = original function, Y2 = nDeriv(Y1, X, X) and Y3 = nDeriv(Y2, X, X).
Then, from the homescreen,
Y1(0) provide the value of y when x = 0,
Y2(0) provide the value of dy/dx when x = 0,
Y3(0) provide the value of d2y/dx2 when x = 0.

Unfortunately, due to limitations of the GC, it cannot check the higher-order derivatives. But this would be a good start, since, if you got the earlier derivatives wrong, the others would most likely be wrong. So if we can guarantee that the earlier derivatives are right, then we are more likely to get the rest correct too.