Sharp EL-W516X Calculation Examples Manual

[Matt Agajanian]

(05-21-2014 07:50 PM)lrdheat Wrote:  Last night, I tried an f(x) that I had in table, and tried, in num-solve, to see if I could use an integral in that application. It worked! If you wish solve an integral from or to a given value, and wish to know what the other value that fills out the range for the integration so that the result equals some desired value, num-solve works! The TI 36pro is truly a $20 dollar pocket wonder.

This works on the HP 39gii as well.

The Prime, of course, is a pocket wonder. I set the display at lowest brightness now so that the battery life will be lengthier.

Could you please give an example of this? That way I can see how this works. Thank you.

[lrdheat]

Hi Matt,

Let's say, in table, I go to choice 2 and make f(x)=(x^2+x+1)/x^(1/2). The 36Pro really "wants" one to enter terms in classic mode, not pretty print. Also wants fractional powers, not the n root key.

I want to find the integral of f(x) from 1 to ? such that the integral=10.

Go to num-solv and make it 10=Integral from 1 to x of f(x). To accomplish this, place curser inside of (),hit table, choose choice 1 which will make the integrand (f()dx. Make it (f(x)), put curser beyond the dx, press enter. This sends you to the solve template. Choose a reasonably sounding "x". Go to solve field, highlight x, enter.

Making a table first (by selecting choice 2 after choosing table) may assist you in making a reasonable guess as this will effect calculation time. When I chose 1 as my guess, it came up with the correct 2.987+ in 54 seconds. When I made a more unreasonable guess of 10, it took 2 minutes 53 seconds. It looks fairly forgiving if your guess is fairly good...remember the guess of "1" took 54 seconds. An excellent guess of 3 took 40 seconds.

None of this is documented in their little guide book. I gave the d/dx and the integral a shot in solve as it didn't say that it couldn't be done...wonder why they (TI) didn't share this as it makes the calculator much more useful in simple calculus!

[lrdheat]

I just reread earlier part of this thread on page 1 and see that CR Haeger made a related discovery, that can also be used to make a table...also useful!

[Matt Agajanian]

Thanks for the techniques. Tried 'em and they work. Although, grabbing the 'f(' string from Table and putting that in the Num-solve equation screen is a bit temperamental. Sometimes it works; sometimes it doesn't and I need to rewrite the right side of the num-solv' equation. I wonder if Classic/Math Print has something to do with that.

[Matt Agajanian]

(04-11-2014 03:25 PM)CR Haeger Wrote:  

(04-11-2014 02:50 PM)lrdheat Wrote:  Just discovered an interesting item that the TI 36pro can do that the CASIO fx-115ES PLUS cannot do...the Casio cannot include a d/dx in a solve problem. The TI can! Enter solve, enter the d/dx, set where x equal to x, enter a guess for x, solve for x, and you get an answer for x when d/dx=0 which will be a min or max of f(x). The variable x now has the number that solve arrived at. If you type in the equation and enter it, you get the value of f(x) at that point. Nicely, since x root of y is available, answers are available for negative numbers where something like 3 root of x is involved.

lrdheat - thanks for the cool tip! I tried this earlier and it stayed busy for a while so I didnt think it would work...

I found these other related (undocumented) operations the TI36X can do:
- Use 2nd Integral in num-solve to solve for uppper, lower limits or even coefficients used in the expression.
- Both 2nd d/dx and Integral can be used in data/formulas and table/edit function --> gives numerical f(x), f'(x) and integral f(x) in the table(s)

Hi.

Got it figured out! Sorry for the mixup.

[Matt Agajanian]

(04-13-2014 06:06 PM)lrdheat Wrote:  A simple example...press table, select choice 2, press clear, and type in the function, shay, sin(x). Hit enter. This takes you to the table setup. You can directly go to num-solve from this screen by pressing 2nd num-solv. Here, you can make 0=d/dx. With curser inside of (), press table, enter choice 1. This brings you back to the num-solv screen. Type an x inside (), make|x=x. This takes you to solve. Try x=1, go down to solve and highlight x and enter. It will come up with ~1.57 if in radians. Quit. This puts you in home screen. Type x and enter, getting ~1.57. Press table, enter choice 1. This brings back the home screen. Type x so that you have f(x) and enter, and you will get f(x)=1 which is f(~1.57).

Of course, making a table can be neat also, and can help with choosing a guess to enter into the solver.

I did find an example that the 36pro balks at in num-solve for finding d/dx=0. This came from hp 15 guide book page 184. The pro36 comes up with domain error when solving d/dx=0 for 5000*(1-e^(-x/20))-200*x. It does make a table without difficulty. Not sure why this happens. The pro36 wasn't bothered with d/dx= for odd number roots where x<0 that I tried...seems like the pro36 solves a good many d/dx=0 functions.

Good luck!

For which calculator are these steps?