Math Help

Archive for May, 2008

In this section of Math Help online, we discuss L’hopital’s Rule which nicely follows Rolle’s Theorem and Mean Value Theorem. 

What is L’Hospital’s Rule?

L’Hopital’s Rule or L’Hospital’s Rule (sometimes just L’Hopital) is a rule permitting the evaluation of the limit of an indeterminate quotient of functions as the quotient of the limits of their derivatives. For example, for sin x, 

 

is an indeterminate of the form 0/0 but it can be evaluated as 

 

Definition of L’Hopital’s Rule

L’Hospital’s Rule is an application of the Mean Value Theorem and lies in the evaluation of 

 

where f(a) = 0 and g(a) = 0. 

The L’Hopital Rule states that if the 

 

is an indeterminate form (such as 0/0), then we can differentiate the numerator and the denominator separately and arrive at an expression that has the same limit as the original problem. Thus, 

 

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Who invented L’Hopital’s Rule?

L’Hopital’s Rule was named after the French Math analyst and geometer, Guillaume Francois Antoine de l’Hopital, Marquis de St Mesme (1661 – 1704). Guillaume Francois Antoine de l’Hopital was the author of the first textbook on differential calculus, but Guillaume Francois Antoine de l’Hopital is believed to have bought the rights to this rule from its discoverer.

Question: Can you help me with a math riddle?

Three bananas were given to two mothers who were with their daugters. Each person had a banana to eat. How is that possible?

thanks sooo much for helping!

Answer: its a grandmother
a mother
and a daughter

get it 2 mothers the grand mother and a mother
and both with their daughters the grandmother was with her daughter (the mother) and the mother was with her daughter ( the daughter)

hope i helped

Math Riddles

Question: MATH…HELP!!! fractions?

on serious answers please. I sukx at math and dont need anymore confusion. Please explain/show how u got your answer so i can learn. thanks people!

3 5/6 divided by 3 1/2 =

quilt magazine gave instructions for making a table proper. A partial list of materials included 1/3 yard red print, 1/2 yard red/blue print, and 3/4 yard blue print. What would be the total yards of material needed for this project?

Pete Hall worked the following hours as a mamger for news.com, 12 1/4, 5 1/4, 8 1/2, 7 1/4. How many total hrs did he work?

Answer: The way to divide fractions is to first convert any mixed numbers to improper fractions and then multiply by the reciprocal (the reciprocal is what you get when you switch the numerator and the denominator). Thus for your first question, you have 3 5/6 ÷ 3 1/2 = 23/6 ÷ 7/2 = 23/6 * 2/7 = 46/42 = 23/21 or 1 2/21.

To add fractions, you must first convert all the fractions so that they have the same denominator, then simply add the numerators. So for your second question, 1/3 + 1/2 + 3/4 = 4/12 + 6/12 + 9/12 = 19/12 or 1 7/12.

If you’re trying to add mixed numbers, you may do so either by converting to improper fractions and then adding, OR you can save yourself some time by adding the fractional portion and the whole number portion seperately, and then recombining. Conceptually, a mixed number is A b/c is A + b/c and so you’re really just using the commutative property of addition to rearrange your numbers before adding. Thus for your third problem: 12 1/4 + 5 1/4 + 8 1/2 + 7 1/4 = 12 + 5 + 8 + 7 + 1/4 + 1/4 + 2/4 + 1/4 = 32+5/4 = 33 1/4

Multiplying Fractions – YourTeacher.com – Math Help