Sharp EL-W516X Calculation Examples Manual

[CR Haeger]

(04-13-2014 06:06 PM)lrdheat Wrote:  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.

Good luck!

Thanks. This is where I was stuck.

[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!

Thanks for the step-through.


Now the question as to which direction Num Solve, looks for a root:

As the 34C, 15C and onward look at the bracket values in the X & Y registers (if I remember correctly), when a single guess value is set in the 36X Pro's num-solve dialog, in what direction does the solver search for a solution?

[lrdheat]

Lightbulb moment!

Just realized why the 36pro balked with solving d/dx (5000*(1-e^(-x/20))-200*x). It doesn't want to solve such a problem for a fractional power. It works like a champ when I make it
5000*(1-(20root e)^-x)-200*x. It solves for f(x)=0 as written originally, but doesn't work with fractional powers when solving for d/dx(f(x)=0.

[lrdheat]

Some functions still yield domain error when setting d/dx=0 BUT, if one bypasses my methodology and just initially goes to the num-solve field and creates 0=d/dx(your equation, even with fractional powers of x), it appears to work consistently. Since the variable x is now stored with the critical point, just go back to num-solv, leave equation as is while getting rid of the d/dx, and make 0=y and solve. You now have the y value at the min or max that you have just found. If you return to home screen, pressing x and enter gives the x of interest, pressing y and entering gives the y value that goes with the x.

Remember to clear variables before calculating further problems using x or y.

[Matt Agajanian]

(04-16-2014 02:28 AM)lrdheat Wrote:  Some functions still yield domain error when setting d/dx=0 BUT, if one bypasses my methodology and just initially goes to the num-solve field and creates 0=d/dx(your equation, even with fractional powers of x), it appears to work consistently. Since the variable x is now stored with the critical point, just go back to num-solv, leave equation as is while getting rid of the d/dx, and make 0=y and solve. You now have the y value at the min or max that you have just found. If you return to home screen, pressing x and enter gives the x of interest, pressing y and entering gives the y value that goes with the x.

Remember to clear variables before calculating further problems using x or y.

Could you please illustrate this by a step-by-step example? That way I can do this exactly the right way without missing or messing up a step. I ask because I have tried this in exactly these steps for 30 minutes and it's not working.

Thanks.

[lrdheat]

Take this function: (5000*(1-e^(-x/20))-200*x). Go to num-solv and directly make the equation
0=d/dx(5000*(1-e^-x/20)-200*x)|x=x. Hit enter. This takes you to the solve template. Enter, say, 3, and solve for x. It will correctly come up with the critical point (happens to be a maximum) of ~4.46. Pick quit. Go directly back to num-solv. Put curser over d/dx and press delete. This takes away d/dx, leaving rest of equation intact. Put curser over the 0 and press x, press again cycling through to get a y. Hit enter. This takes you back to solve template. Leave your x which is populated with the critical value, and solve for y. It comes up with the correct value of ~107. If you wish, press quit. Press x, enter, critical value appears. Press y, enter, y value of critical x appears.

So far, it works on what I've tried without balking. Note that this example did not have to resort to rewriting in terms of (20root of e)^_x.

Pretty cool.

Also nice on 36pro is that cross and dot products of 2D and 3D vectors is supported. Nice probability distributions as well.

Amazing value for ~$20

[Matt Agajanian]

I got you. But, when I go through the first sequence, solving for X, my solution for X is -165.880...

What could I be missing? Perhaps, so I can group it correctly, is -x/20 the exponent of e or is it just (e^-x)/20?

****MY Goof!!

I had the old parentheses pairing/grouping mixup.

I got it now!! I get your 4.46 and 107... results.

Thanks again

[Matt Agajanian]

First off, sorry for the double-post. Interesting TI-36X Pro awkwardness though.

Funny TI-36X Pro behaviour though. When I tried to input the full 0=d/dx(equation)|x=x in the Num-Solve app, everything behaved nicely. BUT, when I tried the approach of using the TABLE app to define the function and then used 0=d/dx(f(x))|x=x as the Num-Solv equation, so as to use that TABLE trick mentioned here earlier, I would get a 'Domain Error' or 'Invalid Data' error.

This TABLE shorthand trick works well with other equations but, when I tried it with the HP-15C, 34C equation we've been mentioning here, the TI-36X Pro has a tantrum.

Why would this be? Is it because of the equation's complexity or is it something else?

Thanks

[lrdheat]

I 'm finding what you are observing to be true...if I'm not sure where to look for extremes, I'll choose table, and enter my function in choice 2, enter, and construct a table in the template that comes up. Then I go to num-solve and rewrite the equation (not a deal breaker, but would be nice to be able to copy and paste) as 0=d/dx(your equation)|x=x! and solve for x entering an appropriate guess. If you are going to check out multiple max/mins, after you get a solution, press enter, press x and store that x into a memory ( I usually use a,b,c,d for multiple points of interest). Go back to num-solve and enter your next guess for your next critical point and store that into a memory register. After finding the critical points, edit the equation in num-solve to read y instead of zero, place curser 1st spot on right of = and press delete. This gets rid of d/dx, and leaves the rest of the equation intact. Press enter to go into solve template. Solve for the multiple points one at a time by recalling the appropriate memory register into x= and solve for y.

Have fun. Other than the WP 34s, this is the only shirt pocket machine that I know of that can do so much! With it's 4 line screen, table, distributions, vector and matrix capabilities, it is a good pocket companion, and for some purposes, is my pocket choice over the 34s. For very high precision, RPN, incredible amount of on board functions, the 34s is head of the class.

[lrdheat]

That is, |x=x in the num-solv....

[Matt Agajanian]

(04-16-2014 07:35 PM)lrdheat Wrote:  I 'm finding what you are observing to be true...if I'm not sure where to look for extremes, I'll choose table, and enter my function in choice 2, enter, and construct a table in the template that comes up. Then I go to num-solve and rewrite the equation (not a deal breaker, but would be nice to be able to copy and paste) as 0=d/dx(your equation)|x=x! and solve for x entering an appropriate guess. If you are going to check out multiple max/mins, after you get a solution, press enter, press x and store that x into a memory ( I usually use a,b,c,d for multiple points of interest). Go back to num-solve and enter your next guess for your next critical point and store that into a memory register. After finding the critical points, edit the equation in num-solve to read y instead of zero, place curser 1st spot on right of = and press delete. This gets rid of d/dx, and leaves the rest of the equation intact. Press enter to go into solve template. Solve for the multiple points one at a time by recalling the appropriate memory register into x= and solve for y.

Have fun. Other than the WP 34s, this is the only shirt pocket machine that I know of that can do so much! With it's 4 line screen, table, distributions, vector and matrix capabilities, it is a good pocket companion, and for some purposes, is my pocket choice over the 34s. For very high precision, RPN, incredible amount of on board functions, the 34s is head of the class.

Thanks for the verification. Yeah, a copy & paste would be helpful and efficient on the 36X Pro and others. Thanks also for the advanced techniques with the additional registers. Very ingenius.

[Matt Agajanian]

Okay, so I'm trying this.

I've got the func in a table and I see there's a root/sign change between 9 and 9.5.

So, I go back to the solver, put in 8 for X and solve but I still get 4.4628...

I've tried to [clear var] before I try to find the next root but, I still get 4.46... for the initial guess of 8. What step or steps am I missing?

[lrdheat]

This is where copy/paste would help. I think you are looking at the equation in table to get an idea of where the max/mins of the function are. The table should suggest one between 4 and 5. What you see on the table between 9 and 10 is a root of the equation, i.e, f(x), not f'(x). The 4.46 that you are seeing in num-solv is where you are finding roots for d/dx of your equation based on your guess educated by your table. After finding your max/mins, then edit the equation in num-solve where 0= is made y=, and put the curser on the first spot right of the =, press delete to get rid of d/dx. Now you can find the value of the function at the x's that produced the max or mins.

[lrdheat]

After finding the value of f(x) i.e. y at the points that produced a max/min, you could, of course solve the equation for x with y equals 0 to get your root at ~9.28.

[Matt Agajanian]

Yeah, I got the gist of what I was dealing with when I plotted the 34C/15C equation, f'(x) and f''(x). Once I saw the plots, I caught on to where to go from there.

[lrdheat]

On the 36pro, I find that the calculator, when solving for d/dx f(x)=0, it is happiest when an equation is entered in classic mode. Pretty print fractions, and especially pretty print n roots seem to be more costly in # characters allowed and acceptability. Classic entry of fractions and fractional powers seem much less restricted...so much less so that I prefer setting the equation up in table to verify that the function behaves as I expect, and find reasonable guesses. Then, it's a snap to go to num-solve, set 0=d/dx then hit table, choice 1 to enter f(, make it f(x), and solve for x=x. Easy then to find f(x) for critical points found.

[Matt Agajanian]

(04-27-2014 05:19 AM)lrdheat Wrote:  On the 36pro, I find that the calculator, when solving for d/dx f(x)=0, it is happiest when an equation is entered in classic mode. Pretty print fractions, and especially pretty print n roots seem to be more costly in # characters allowed and acceptability. Classic entry of fractions and fractional powers seem much less restricted...so much less so that I prefer setting the equation up in table to verify that the function behaves as I expect, and find reasonable guesses. Then, it's a snap to go to num-solve, set 0=d/dx then hit table, choice 1 to enter f(, make it f(x), and solve for x=x. Easy then to find f(x) for critical points found.

Quite the illuminating point. Perhaps there is some more intensive memory/punctuation token demands in MathPrint than Classic that is not evident in the manual.

Thanks for that behind-the-scenes tip.

[lrdheat]

Decided to see if MathPrint is costly in calculation time on the TI 36Pro beyond presenting difficulties in the num-solve application while using d/dx. It is!

When taking the simple integral of 3rd root of 2*x from 0 to 4 in MathPrint, the calculation took about 38 seconds. In classic entry mode, the same calculation was accomplished in about 21 seconds.

[lrdheat]

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.

[CR Haeger]

(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.

Yep I noticed this worked as well. Try it with other variables IN f(x) and you can solve for them as well.