     Van / facebook.com/LearningCalculus / 2015
     L'Hopitals rule (قاعدة لوبيتال): Preamble (مقدمة) (لانهاية)

     Test these statements by removing '$' characters.

kill(all)$ minf;
isLimitMinf(L) := is(equal(L,minf))$ isLimitMinf(minf)$isLimitMinf(0)$isLimitMinf(inf)$
isLimitSifr(L) := is(equal(L,0))$ isLimitSifr(minf)$isLimitSifr(0)$isLimitSifr(inf)$
isLimitInf(L) := is(equal(L,inf))$ isLimitInf(minf)$isLimitInf(0)$isLimitInf(inf)$

OR(a,b):=a or b$

isLimitMinfOrSifrOrInf(L):=is(OR(OR(isLimitMinf(L),isLimitSifr(L)),isLimitInf(L)))$

isLHopitalApplicable(L):= isLimitMinfOrSifrOrInf(L)$

     L'Hopitals rule may be only used if BOTH conditions are true:

isLHopitalApplicable(limit(f(x),x,1))$
isLHopitalApplicable(limit(g(x),x,1))$

f(x):=(sqrt(9*x-1)^(1/3) + sqrt(5*x-1) - 4);
g(x):=(x^2 - 1);

u(x):=''(f(x)/g(x));

'limit(((9*x-1)^(1/6)+sqrt(5*x-1)-4)/(x^2-1),x,1) ;
van=facebook.com/LearningCalculus;

'limit(((9*x-1)^(1/6)+sqrt(5*x-1)-4)/(x^2-1),x,1) ;

A:isLHopitalApplicable(limit(f(x),x,0))$
B:isLHopitalApplicable(limit(g(x),x,0))$
is(A) and is(B);

u(x):=f(x)/g(x)$ u(x);

limit(f(x)/g(x),x,1,minus);

limit(f(x)/g(x),x,1,plus);