To which I would add this:
A graduate student of Trinity
Computed the square of infinity.
But it gave him the fidgets
To put down the digits,
So he dropped math and took up divinity.
- Anonymous
[2.25] Factor on complex
i
to show polynomial complex coefficients
The CAS automatic simplification perturbs complex coefficients of polynomials, for example,
[1]
(
a + bi
)
x
2
+
(
c + di
)
x + e + fi
becomes
ax
2
+ cx + e +
bx
2
+ dx + f
$
i
Use the factor() function to display coefficients associated with the independent variable, as in [1]
above. For this example, use
factor(a*x^2+c*x+e+(b*x^2+d*x+f)*¡,¡)
where 'i' is the complex 'i', not the alphanumeric 'i'.
[2.26] limit() fails with piecewise functions
The CAS has problems with limits of piece-wise functions defined with when(). For example,
limit(when(x=0,1,sin(x)/x),x,0)
returns itself, instead of the correct limit of 1. This problem occurs with limits of the form
limit(when(x=a,b,f(x)),x,0)
only when the first when() argument is an equality, and the complete limit at zero is taken. To get
around this failure, use an independent variable of, for example, k-1, and evaluate the limit at 1. The
original example becomes
limit(when(k-1=0,1,sin(k-1)/(k-1)),k,1 )
which correctly returns 1.
(Credit to Martin Daveluy)
2 - 18
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