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

##### Solving 0/0 and ∞/∞ limit problems using L'Hospital's Rule.

### This page exists due to effort of the following persons:

**Author**- Anton - Solving limit problems using L'Hospital's Rule
**Translation author**- Timur - Solving limit problems using L'Hospital's Rule
**Created using the work of**- Anton - Solving 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 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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