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# Solving limit problems using L'Hospital's Rule

##### Solving 0/0 and ∞/∞ limit problems using L'Hospital's Rule.
Anton2011-08-23 21:34:00

This calculator tries to solve 0/0 or ∞/∞ limit problems using L'Hospital's Rule. Below are some theory notes.

##### Solving limit problems using L'Hospital's Rule

L'Hospital's Rule

If the following are true:

limits of f(x) and g(x) are equal and are zero or infinity:
$\lim_{x\to a}{f(x)}=\lim_{x\to a}{g(x)}=0$ or
$\lim_{x\to a}{f(x)}=\lim_{x\to a}{g(x)}=\infty$

functions g(x) and f(x) have derivatives near point a

derivative of g(x) is not zero at point a: $g'(x)!= 0$;

and there exists limit of derivatives: $\lim_{x\to a}{\frac{f'(x)}{g'(x)}}$

then there exists limit of f(x) and g(x): $\lim_{x\to a}{\frac{f(x)}{g(x)}}$, and it is equal to limit of derivatives : $\lim_{x\to a}{\frac{f'(x)}{g'(x)}}$

For function you can use the following syntax:

Operations:
- subtraction
* multiplication
/ division
^ power

Functions:
sqrt - square root
rootp - n-th root, f.e. root3(x) is a cubic root
lb - logarithm with base 2
lg - logarithm with base 10
ln - natural logarithm with base 8
logp - logarithm base p, f.e. log7(x)
sin - sine
cos - cosine
tg - tangent
ctg - cotangent
sec - secant
cosec - cosecant
arcsin - arcsine
arccos - arccosine
arctg - arctangent
arcctg - arccotangent
arcsec - arcsecant
arccosec - arccosecant
versin - versine
vercos - vercosine
haversin - haversine
exsec - exsecant
excsc - excosecant
sh - hyperbolic sine
ch - hyperbolic sine
th - hyperbolic tangent
cth - hyperbolic cotangent
sech - hyperbolic secant
csch - hyperbolic cosecant
abs - absolute value (module)
sgn - signum (sign)

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