New HP 50g Questions

Hi,

I hardly bought the HP 50g yesterday which is my first HP calculator,
with the TI-89 Titanium being my close companion up to that point. So
as a beginner to RPN and HP calculators, I have a few questions that
hopefully arise from my ignorance and not the fault of the calculator
(which I heard is marvelous at math).

1. Why doesn't the HP integrate (x+1)^4 as 1/5*(x+1)^5 which is the
textbook answer?
2. How do I do a fourier series expansion? For example, expand x from
[-pi,pi] to the 7th oder.
3. I am confused as to how to use the series command. How do I expand
ln(x)?
4. The HP does not symbolically compute integral of sin(x)^3/x^3 from
0 to infinity. This is understandable because I don't think my TI can
do it either. However, I cannot get a numerical answer from the HP. I
get an overflow message. The answer is supposed to be 3*pi/8.
5. How do I use the with bar in RPN mode? For example, how would I
compute x+1|x=3? Also, how do I use the with bar with inequalities?
For example, sin(x)|x>0?
6. How do I solve sin(x)=1 (I know how to do that using the solve
command), but how do I evaluate it for various integers? Perhaps this
question links with the above question.
7. How do I use the solve command to solve multiple non-linear
equations. For example, x^2-2x+y=3 and 4x-y=1.
8. I was experimenting with the step-by-step mode for the integral 1/
root(x^2-1), but it made no sense. It just said rational fraction for
most of the integrals or square root, but did not show any
substitution or any techniques. It is not a major problem, but I was
just wondering.
9. Why does 1/(x-1) show a vertical line at asymptote x=1 in the
graph. The 89 omits this so is there a way to omit it from the graph
on the HP? This is not a major issue.
10. Is there a simple way to graph vertical lines such as x=2? I mean
without using any "tricks" such as 9E999(x-2).
11. How do I test equalities? For example, how do I know if 1=2 or
(x^2-1)/(x-1)=x+1 are true statements or false statements?
12. Do I have the latest ROM version out of the box? I believe so
because the 50g is the latest HP calculator and the last ROM was
released in 2006 which is when the HP was released, correct? I have
not yet opened the CD so I don't know if it has an updator or anything
with it that can tell me.

Thanks in advance! I hope to become a skilled HP user like you!

.

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