Solving limit problems using L'Hospital's Rule
Solving 0/0 and ∞/∞ limit problems using L'Hospital's Rule.
This calculator tries to solve 0/0 or ∞/∞ limit problems using L'Hospital's Rule. Below are some theory notes.
L'Hospital's Rule
If the following are true:
limits of f(x) and g(x) are equal and are zero or infinity:
or
functions g(x) and f(x) have derivatives near point a
derivative of g(x) is not zero at point a: ;
and there exists limit of derivatives:
then there exists limit of f(x) and g(x): , and it is equal to limit of derivatives :
For function, you can use the following syntax:
Operations:
+ addition
- 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 e
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 cosine
th - hyperbolic tangent
cth - hyperbolic cotangent
sech - hyperbolic secant
csch - hyperbolic cosecant
abs - absolute value (module)
sgn - signum (sign)
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