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Solving limit problems using L'Hospital's Rule

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

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Anton

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Timur

Created: 2011-08-23 21:34:00, Last updated: 2021-02-10 05:31:38
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This content is licensed under Creative Commons Attribution/Share-Alike License 3.0 (Unported). That means you may freely redistribute or modify this content under the same license conditions and must attribute the original author by placing a hyperlink from your site to this work https://planetcalc.com/1036/. Also, please do not modify any references to the original work (if any) contained in this content.

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

PLANETCALC, Solving limit problems using L'Hospital's Rule

Solving limit problems using L'Hospital's Rule

Syntax: + - / * ^ pi sin cosec cos tg ctg sech sec arcsin arccosec arccos arctg arcctg arcsec exp lb lg ln versin vercos haversin exsec excsc sqrt sh ch th cth csch
Digits after the decimal point: 2
L'Hospital's Rule
 
Limit at the point
 



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:
+ 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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PLANETCALC, Solving limit problems using L'Hospital's Rule
Anton2021-02-10 05:31:38

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