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Polish notation : exercice 2

This time, we want to define function f such as :



First method, using direct polish notation from the beginning to the end

This one is a bit tricky... Is it a sum ? A difference ? Obviously it could be both, but seeing it as a sum makes things easier... If indeed we wanted to see it as a difference, then we would need to interpret f(x) like this :



But seeing it as a sum, we see it like that :



In the second case, the operators stay the same as the original, intended, formula, and moreover the parenthesis are actually not needed... I just put it there to view more naturally the two members to be summed.

Note that the function arctan is named atan in Grapher Touch, and is to be found in place of tan function when the modifier 2nd is enabled.

So let's indicate the formula is a sum :



Then the left operand of the sum is a difference, so we press :



Then the left operand of the difference is the arc-tangent of something :



Then we have to enter 1/(2x^2), we could consider it a quotient, but we can also consider it the inverse of 2 x^2, which itself is a product... So it comes :



Now we have to enter arctan(x/(x-1)), which is obtained with :



and I let you guess the end... The correction can be found in the video for this exercice...

Second method : using touchplot >= 2.2 new features, but not the novelties in touchplot 3.2

Of course, the first method still works, but typically you probably will use touchplot 2.2 (or later) like this :

first enter arctan(1/(2x^2)) :



or (little variant) :



Formula could be finished and validated such as it is, but you can complete it with :



then the second member of the sum :



then



and the third member of the expression remains to be entered, which could be done like that :



The video that goes along with this exercice shows first how to enter this formula with direct polish notation and secondly how this formula could be entering avoiding completely polish notation, and using the selection scheme of TouchPlot 3.2 new editor. (See the page about the 3.2 new editor.)