Thread: Numbers e and pi

I found the following 2 questions regarding e and pi in the special topics of my precalculus math book.

(1) e^(pi) + pi^(e) =

(2) e^(pi)^(e) + pi^(e)^(pi) =

Originally Posted by sologuitar

I found the following 2 questions regarding e and pi in the special topics of my precalculus math book.

(1) e^(pi) + pi^(e) =

(2) e^(pi)^(e) + pi^(e)^(pi) =

So, what's your question?

What's so special about those results ? I typed into google and it doesn't show anything particular ...
Or are you supposed to calculate it without a calculator ? Or simplify it ?

There is nothing special about them. I suspect that they are just exercises in using your calculator. Probably your calculator has a "[itex]\pi[/itex]" key. If not, you can always use [itex]\pi= 4tan^{-1}(1)[/itex] (with your calculator in radian mode, of course). For "e" use either the " key to find or use the "inverse" "ln" keys.

I suspect that they are just exercises in using your calculator.

In the special topics of a precalculus maths book ?

I don't why this is called "special topics" by the author.
Now, can this be done without a calculator?

Originally Posted by sologuitar

I don't why this is called "special topics" by the author.
Now, can this be done without a calculator?

No, unless have have an integrated floating point unit processor in your cerebral cortex. And even with infinite processing power, you would not be able to get the exact answer, since and are irrationnal. Thus, you must use a calculator to get the best "approached" value.