calculator
I'm looking for a calculator that shows a full answer regardless of it's length.
For example the assignment 2^1000 will output: 1,07150860718626732094842504906e+301.
Windows calculator shows me that amount because else it won't fit the display.
So the question is:
Is there a calculator out there that shows the full answer instead of shortening it?
This is what I would do to calculate $e^x$ with perfect 8-digit accuracy.
Take $\lfloor x\rfloor$ and $b = x - \lfloor x\rfloor$, the whole and fractional parts respectively. ($e^x = e^{\lfloor x \rfloor + (x - \lfloor x\rfloor)} = e^{\lfloor x \rfloor} e^{x - \lfloor x \rfloor}$)
Use the $(((b/4 + 1)b/3 + 1)b/2 + 1)b + 1$ pattern to calculate $e^{x - \lfloor x\rfloor}$. (If the fractional part of the exponent is .4 or less, only terms up to $b/7$ are needed for 8-digit accuracy. Worst-case scenario ($b \rightarrow 1$) terms up to $b/10$ are needed.) This method is easy to implement on a simple calculator, especially ones with a memory slot to quickly reinsert $b$.
When that is finished, multiply by $e$ ($\approx 2.71828183$ by memorization) and press the equals button $\lfloor x\rfloor$ times to repeat multiply. The result is $e^x$.
I've analyzed the number of terms required for full accuracy. Here is the chart (click to view full image):
Basically, if terms up to $b/t$ are needed to fully calculate $e^x$ up to 8-digit precision (7 digits after the decimal point), accounting for rounding (the $\frac{1}{2}$ term), the relation between $x$ and $t$ is given by $\sqrt[t]{\frac{1}{2}10^{-7}t!} = x$.
You used the if operator incorrectly. The format is
if( condition, what to do if True, what to do if False)
But you put another condition in the place of "what to do if false".
Here's an example: I want a function which is equal to $3x$ between $x=1$ and $x=4$, is equal to $x+8$ between $x=4$ and $x=5$, and is undefined otherwise. The code could be
if(x>5, ln(0), if(x>4, x+8, if(x>1, 3*x, ln(0) ) ) )
Here I'm using $\ln(0)$ with the hope that it will simply produce no output for the corresponding range, rather than halt the entire computation. Don't have the app (or iPad for that matter), so can't tell for sure.
Best Answer
If you don't mind a web-based solution, wolframalpha.com will do that for you:
outputs: