kill(all)$

      Van = facebook.com/LearningCalculus / 2017
      L'Hopitals rule: Preamble

      Test these statements by removing '$' characters.

kill(all)$ minf$
OR(a,b) := a or b$ AND(a,b) := a and b$
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)$
isLimitMinfOrSifrOrInf(L):=is(OR(OR(isLimitMinf(L),isLimitSifr(L)),isLimitInf(L)))$
isLHopitalApplicable(L):= isLimitMinfOrSifrOrInf(L)$

f(x):=x^(1/4)-x^(1/6)$
g(x):=x^(1/8)-x^(1/12)$
h(x):= f(x)/g(x)$

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

A:isLHopitalApplicable(limit(f(x),x,1))$
B:isLHopitalApplicable(limit(g(x),x,1))$
is(A) and is(B);

f(x)/g(x);

diff(f(x),x); limit(%,x,1);

diff(g(x),x); limit(%,x,1);

(1/12)/(1/24);

limit(h(x),x,1);

limit(h(x),x,a);