XProfan

English

p.specht

Uni-Anfängern becomes in the first maths-Unterricht gladly The harmless erscheinende Gleichung y=x^x pictured, together with the schlichten Please, The Kursteilnehmer like still so nice his and these function until next deadline to x aufzulösen. students unterschätzen these task in the rule vast and receive so your erstes I see!-experience.
Your mathematischen names sustained The Gleichung ditto on these point: on Unis in the anglikanischen Sprachraum go The Erstsemestrigen üblicherweise "Sophomores" (altgriechisch about 'unbedarfter Dorftrottel') called, it deals itself therefore integrally official around the undertow. SOPHOMORE-function: Y = X ^ X.

in the numerischen practice becomes NOT to x umgestellt (= invertiert), separate Newton-Raphson on Xneu = x - (F(x)-y)/(d_F(X)/d_x)) angesetzt. around the nötige amount Iterationen so nieder How possible To hold ought to The Ableitung of x^x - y = 0 famous his, and the yields itself lt. tables To x^x*(ln(x)+1).

Compile Mark Separation

Window Title "Iterative Solution the Sophomore-Gleichung Y=X^X"
Window Style 24:set("decimals",17):font 2:CLS:declare x!,y!,xneu!,i&
REPEAT :print "\n Y=X^X Ges: X for Y=?",:input y!

if y!<=0:print " function not More honest-wertig!":beep:continue

elseif y!<0.7:print " worth not monoton aufsteigenden branch the function!"

    beep:continue:endif:xneu!=10:i&=0
    Repeat:inc i&:x!=xneu!
    xneu!=x! - (x!^x!-y!)/(x!^x!*(ln(x!)+1))

until (abs(xneu!-x!)<(10^-15)) or (i&>2000)

if i&<=2000:print " x = ";x!," nach",i&,"Läufen. Probe: X^X= ";x!^x!

    else : print " *** Error: not konvergent! ***":beep:endif

UNTIL %key=27:END