Introduction to L'Hopital's Rule Calculator:
L'Hopital's Rule Calculator is an amazing tool that helps you to calculate the indeterminate form of function. It is used to evaluate the limit of the special type of function which are present in the form of 0/0 or ∞/∞ or 0x∞, ∞x∞.
When you calculate the indeterminate form problem by hand you may get confused because of complex function or you don't know the rule about how to solve these problems using l'hopital method. To avoid the tedious effort of solving you need a calculator like our L'hospital calculator that provides you solution without doing any calculation.
What is L'Hopital's Rule?
L`Hopital is a process that is used to find the limit of indeterminate form of functions using differential methods in calculus. If you want to evaluate the limit of these functions directly you cannot find the solution because it is given an undefined solution.
The indeterminate form of function has different forms like 0/0 or ∞/∞ or 0x∞, ∞x∞ and if your function has any of this form then you can apply the l`hopital method to get a solution easily.
Rule of L`Hopital:
The rule of l`hopital is consist of two function f(x) and g(x) which are differentiable functions such as f`(x) and g`(x) and both have a limx→cf(x)=0 and limx→cg(x)=0, then
$$ \lim_{x \to c} \frac{f(x)}{g(x)} \;=\; \lim_{x \to c} \frac{f’(x)}{g’(x)} $$
How to Calculate L'Hopital's Rule?
For the Calculation of a limit function using L'Hôpital's rule you need to understand the different forms of indeterminate form which is 0/0 or ∞/∞ or or 0x∞, ∞x∞. Here’s a step-by-step guide on which you know about how to apply L'Hôpital's process.
Step 1:
Determine the function if the limit function that you want to evaluate is in the form 0/0 or ∞/∞.
Step 2:
Only you can apply the l`hopital rule if the given function follow 0/0 or ∞/∞ form.
Step 3:
To reduce the indeterminate form, differentiate the given function and it should ensure that f(x) and g(x) are differentiable separate at the numerator and denominator.
Step 4:
Again evaluate the limit in f`(x) , if the function 's indeterminate form reduces then you can simply apply the limit and get a solution.Otherwise you need to again differentiate the function with respect to x and then again check the limit.
Step 5:
Repeat this process if needed until the limit can be evaluated directly or the determined form does not exist in the given function.
Solved Example Of L'Hopital's Rule:
The solved example of indeterminate form of limit function l'hopital's rule calculator with steps gives you more clarity about its calculation process.
Example: Find the indeterminate form of function
$$ \lim_{x \to c} \frac{1 - cos\; x}{x} $$
Solution:
Determine the given function,
$$ \lim_{x \to 0} \frac{1 - cos\; x}{x} $$
Apply the limit to check it has indeterminate form or not,
$$ \lim_{x \to 0} \frac{1 - cos\;x}{x} \;=\; \frac{0}{0}\; form $$
=0/0 form
So apply l`hopital rule in which you differentiate the function with respect to x (differentiate numerator and denominator separately without following regular rule of derivation)
$$ =\; \lim_{x \to 0} \frac{\frac{d}{dx}(1 - cos\; x)}{\frac{d}{dx}(x)} $$
Again check function indeterminate form reduce or not by applying the limit,
$$ \lim_{x \to 0} \frac{sin\; x}{1} $$
Now you can apply limit because function is no more undefine function,
$$ \frac{\lim_{x \to 0} sin\; x}{\lim_{x \to 0} 1} \;=\; \frac{0}{1} $$
The result of given indeterminate function is,
$$ \frac{\lim_{x \to 0} sin\; x}{\lim_{x \to 0} 1} \;=\; \frac{0}{1} \;=\; 0 $$
How to Solve L Hospital Rule Calculator?
L'hopital calculator has a simply layout so you just need to enter your problem in this calculate to get a solution in an easy method. Follow our guidelines before using it. These guidelines are:
- Enter the limit function in the input field that you want to evaluate.
- Enter the limit point value in the input box.
- Add the variable of differentiate through which you want to find limit function
- Select the type of indeterminate form of given limit function.
- Review the given function value before hitting the calculate button to start the evaluation process in thel'hospital's rule calculator.
- Click the “Calculate” button to get the solution of your given limit function problem in L'Hopital's Rule.
- If you want to try out our professional tool for the first time then you must try out the loud example of l'hopital limit function to learn more about it.
- Click on the “Recalculate” button to get a new page to find more example solutions of limit function problems.
Output from L Hopital Rule Calculator:
L'Hopital's Rule Calculator gives you the solution to a given limit function question when you add the input into it. It may be included as:
Result option
When you click on the result option it gives you a solution to the l'hopital problem.
Possible steps
It provides you with a solution to the l'hopital's rule problem where all the calculations are mentioned in steps.
Advantages of L'Hopital Calculator:
L hospital rule calculator provides a ton of advantages that you get when you calculate the indeterminate form of limit problems to get solutions. These advantages are:
- L hopital rule calculator is a free tool that enables you to evaluate the limit indeterminate problem with a solution.
- It is a manageable tool that can solve different types of indeterminate form to find the limit function using the l'Hopital rule.
- Our tool helps you to get a stronghold on the l'hopital rule method when you use it for practice.
- L'hospital's rule calculator saves the time that you consume on the calculation of the limit function without applying L'Hopital's rule manually but it helps you to evaluate the given function limit in a couple of minutes.
- L'Hopital's Rule Calculator is a reliable tool that provides you accurate solutions when you use it to calculate the limit function problems without error.
- L hospital rule calculator gives the solution without a sign-in condition so you can use it anywhere through the internet.
