\displaystyle \lim_{x \to APPROACHES_TEXT} \frac{NUMERATOR}{DENOMINATOR} = {?}
SLN_NUMERATOR / SLN_DENOMINATOR
L'Hopital's rule states that since evaluating
\displaystyle \lim_{x \to APPROACHES_TEXT} \frac{NUMERATOR}{DENOMINATOR} = INDETERMINATE_FORM
,
if \displaystyle \lim_{x \to APPROACHES_TEXT} \frac{\frac{d}{dx} (NUMERATOR)}{\frac{d}{dx} (DENOMINATOR)}
exists, evaluating it will give us the actual limit.
Repeat this process until evaluating the limit will not result in an indeterminate form:
Since evaluating the limit at this point still results in INDETERMINATE_FORM
, we must apply L'Hopital's rule again:
\displaystyle\frac{\frac{d}{dx} (STEP[0])}{\frac{d}{dx} (STEP[1])} =
\frac{STEPS[N+1][0]}{STEPS[N+1][1]}
Evaluate the limit:
\displaystyle \lim_{x \to APPROACHES_TEXT} \frac{SLN_NUMERATOR_TEXT.text()}{SLN_DENOMINATOR_TEXT.text()}
= \frac{SLN_NUMERATOR_TEXT.text().replace("x", "(0)")}{SLN_DENOMINATOR_TEXT.text().replace("x", "(0)")} =
\frac{SLN_NUMERATOR}{SLN_DENOMINATOR}
= fractionReduce( SLN_NUMERATOR, SLN_DENOMINATOR )