Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. (a) consider the function f(x)=(ex ?1)/x. use l’

(a) Consider the function f(x)=(ex ?1)/x. Use l’Hˆopital’s rule to show that lim f(x) = 1...

60.2K

Verified Solution

Question

Advance Math

(a) Consider the function f(x)=(ex ?1)/x.

Use l’Hˆopital’s rule to show that lim f(x) = 1 when xapproaches 0

(b) Check this result empirically by writing a program tocompute f(x) for x = 10?k, k = 1,...,15. Do your results agree withtheoretical expectations? Explain why.

(c) Perform the experiment in part b again, this time using themathematically equivalent formulation, f(x)=(ex?1)/log(ex), evaluated as indicated, with nosimplification. If this works any better, can you explain why?

Please ignore the programming part. I am interested in knowingwhy this happens.

Answer & Explanation Solved by verified expert
4.1 Ratings (709 Votes)
By LHopitals rule in any limit valueit in indeterminate form so that is 00 here we canapplyLHopitals rule so that we get it in determinedlimit valueBy this rule we can differentiate fx and gx separately andthen it is in ratio we can evaluate if still it is same    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Zin AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Q

On the Miller Park Stadium project who had the ultimate responsibility to make sure that wind...

Civil Engineering
Q

In the West, we value developing an autonomous and individualistic personality. In many Eastern cultures, “Groupthink” is...

Psychology
Q

A firm produces sunglasses on a single production line served during one daily shift. The total...

General Management
Q

certain birth defects and syndromes are polygenetic in nature. typically , fhe chance that an offspring...

Advance Math
Q

Express the answer in scientific notation An ore deposit consisting of chert and hematite occurs...

Physics
Q

A B and C are three rafts floating in a river such that they always...

Physics
Q

Consider the following functions Step 4 of 4 Find Answer How to enter your answer...

Algebra
Q

Question 10 of 10

Accounting
Q

Consider the following facts: Company A acquires land for $96,000 cash. Additional costs are as...

Accounting
Q

A company reports the following fixed budget based on expected production and sales of 2,000...

Accounting
Q

Help will thumbs up! Bramble, Inc. decided on January 1 to...

Accounting
Q

Exchange-Traded Funds (ETFs) There are partial credits available for this question since the question is...

Finance