Register to reply

Limits, infinity, and my calculator...

by GeoMike
Tags: calculator, infinity, limits
Share this thread:
Sep8-06, 02:43 PM
P: 70
I understand that the limit of sec^2(x) as x approaches pi/2 is infinity (increasing without bound), and I understand the meaning of this in terms of the epsilon-delta definition of an infinite limit.
I also understand why the limit of sec(x) as x approaches pi/2 doesn't exist.

What I'm a bit "sketchy" on is why my calculator (Ti-89 Titanium) displayes "infinity" as the value for sec^2(pi/2) and "undefined" for sec(pi/2) (not when evaluating the limit, but just when evaluating the function at that value). Why aren't sec^2(pi/2) and sec(pi/2) both displayed as "undefined"? Neither sec^2(x) nor sec(x) have a defined value at pi/2, do they? The fact that in one case the limit exists doesn't seem to have any effect on the value of either function at pi/2 (my book stresses the point that the limit of f(x) as x->a doesn't necessarily mean that f(a) = L, f(a) need not even exist -- which seems to be the case here)

I'm also confused because there is a bit of ambiguity in my mind concerning "1/0" and "infinity"

Can anyone help me understand this...?
Phys.Org News Partner Science news on
'Smart material' chin strap harvests energy from chewing
King Richard III died painfully on battlefield
Capturing ancient Maya sites from both a rat's and a 'bat's eye view'
Sep8-06, 03:55 PM
Sci Advisor
P: 1,253
When your calculator evaluates sec(pi/2)^2 it replaces the undefined value with the limit. When your calculator evalutes sec(pi/2) there is no limit since the function goes to negative infinity on one side of pi/2 and to positive infinity on the other side, so the calculator just says undefined.

At least, that's how the calculator works. It's only a quirk of its operation. It has nothing to do with the function's actual value at pi/2, which is not defined in either case.
Sep8-06, 04:36 PM
P: 70
Thank you, that cleared a lot up for me.

Register to reply

Related Discussions
Integral Limits: Infinity. Calculus & Beyond Homework 5
Limits, infinity, and cardinality (oh, and integrals too) Calculus 11
Limits of polynomials at infinity Calculus 3
Limits at infinity Calculus & Beyond Homework 2
Infinity Limits Calculus & Beyond Homework 1