Tuesday, July 14, 2015

Advanced Math Solutions – Limits Calculator, L’Hopital’s Rule

In the previous posts, we have talked about different ways to find the limit of a function. We have gone over factoring, functions with square roots, and rational functions. What happens when none of those options work? That is when L’Hopital’s Rule comes in.

L’Hopital’s Rule:
If \lim_{x\to a}(\frac{f(x)}{g(x)})=\frac{0}{0}  or  \lim_{x\to a}(\frac{f(x)}{g(x)})=\frac{\pm\infty}{\pm\infty}, where a is finite or \pm\infty,
Then \lim_{x\to a}(\frac{f(x)}{g(x)})=\lim_{x\to a}(\frac{f^{'}(x)}{g^{'}(x)})

What does L’Hopital’s Rule mean?

If f(x) and g(x) are differentiable and if the limit of \frac{f(x)}{g(x)} as x approaches a is \frac{0}{0} or \frac{\pm\infty}{\pm\infty}, then we take the derivative of the numerator and the derivative of the denominator,  \frac{f^{'}(x)}{g^{'}(x)} . The limit of \frac{f(x)}{g(x)} as x approaches a is equal to the limit of \frac{f^{'}(x)}{g^{'}(x)} as x approaches a.

When can you use L’Hopital’s Rule?
1. When the limit is in the indeterminate form of \frac{0}{0} or \frac{\pm\infty}{\pm\infty}
2. Sometimes when the limit is in the other indeterminate forms
3. When the function has an exponent and the limit is an indeterminate form

Here we will work out the first problem step by step (click here):

Try Substitution
We get an indeterminate form of \frac{0}{0}

Take the derivative of the numerator:

Take the derivative of the denominator:

Simplify the function:
\lim _{x\to \:-3}\left(\frac{\frac{x}{\sqrt{x^2+16}}}{1}\right)=\lim _{x\to \:-3}\left(\frac{x}{\sqrt{x^2+16}}\right)

Substitution:
\frac{-3}{\sqrt{\left(-3\right)^2+16}}=-\frac{3}{5}

L’Hopital’s rule is an easy way to find the limit, as long as the derivatives aren’t too tedious. It is important to remember to double check your work. I found myself a lot of times making simple errors, like forgetting the chain rule or changing signs. Next week we will talk about the chain rule for limits.

Fun fact: It is believed that Johann (John) Bernoulli discovered L’Hopital’s Rule.

Until next time,
Leah

1. How can appy the hospital rule using the symbolab?
I mean how can I selected to use the rule?

2. This program is a very good help in
Yet it is still better than the program resolved by methods used in the Portuguese education system that does not include the rule L'Hopital

3. Thanks. It's a good post. And in competition exams mostly the questions of calculus are picked from this rule. But if you illustrate product rule, power rule. Then it will be a better post.

4. The limit of $\frac{f\left(x\right)}{g\left(x\right)}$ as x approaches a is equal to the limit of $\frac{f^'\left(x\right)}{g^'\left(x\right)}$ as x approaches a. 250-430 braindumps

5. Very nice & help full information.....
210-065 Dumps PDF

6. I think that homework does not have to be hard, if you agree with me I recommend that you check out this blog article for some additional useful info.

7. Students can easily get the Uk Students Assignment Help services? StudentsAssignmentHelp.com is the best place for you. We are continue giving quality work for all our clients and make sure that all their academic needs are fulfilled. We are giving a varied range of academic writing help at a low price.

9. This is quality work. Even though the topic is tangled on its own, your blog made it fun. Looking forward to similar topics in the future.
Are you looking for the Technology, Business, Fitness and Education News - Needynews is the one spot solution for all real-time updated news.

10. Mainkan di situs Togelplus dan dapatkan promo hadiah menarik

11. I would like to thank you for the high level and informative article with us.
I hope you and we will sharing more idea's and the keep writing more like the this one.
If you Search for Assignment Provider then contact with us.

12. It is very informative. You have given a fresh outlook on the topic. I would definitely share this on other platforms as well. complete my assignment

13. Disini kami akan berbagi informasi tentang cara menggugurkan hamil dengan cepat dan akurat dengan menggunakan obat aborsi . Mungkin Anda adalah salah satu yang ingin mencari tahu obat penggugur kandungan yang aman dan terbukti ampuh , agar dapat membantu anda untuk melakukan proses cara mencegah kehamilan yang tidak Anda inginkan . Saat ini memang banyak sekali situs yang jual obat aborsi secara online . Namun anda harus lebih cermat dalam memilih . Misoprostol adalah obat menggugurkan kandungan terbaik untuk menginduksi rahim , dan ini bisa anda gunakan untuk memperlancar haid atau sebagai obat telat datang bulan

14. obat aborsi And I'm animated reading your article. But should remark on some general things, the website style is perfect; the articles are great. Thanks for the ton of tangible and attainable help.
obat penggugur kandungan

15. Such a beautiful information shared in this article and further you want to enhance your knowledge please read about Driver Tonic Activation Code whereby you can active driver tonic and update all drivers.