Indeterminate forms in Mathematics
Reference & Education → Education
- Author Isabella Evans Isabella Evans
- Published September 20, 2011
- Word count 407
An indeterminate form in mathematics is an algebraic expression whose value cannot be determined definitely. There are 7 known indeterminate forms, which are : 00, 0/0, 1∞, ∞ − ∞, ∞/∞, 0 × ∞, and ∞0.
When trying to evaluate an algebraic expression or function, we use limits if it is not possible to determine the exact value. That is, we try to find the limiting value of the function at some point. Yet, at times we arrive at certain forms of limits for which, merely finding the limiting behaviour of individual parts is not sufficient to actually determine the overall limit. These forms are said to be indeterminate. For example, the limit of the function f(x)/g(x) would give rise to the form 0/0 if the individual limits of each function f(x) and g(x) are zero for some limiting value of x. This is an indeterminate form since the value of the overall limit actually depends on the limiting behavior of the combination of the two functions, and not on the individual functions.
Many mathematicians have attempted to arrive at feasible methods to find or solve these indeterminate forms. French mathematician Guillaume de L'Hôpital is probably the most successful of all, introducing the L’Hopital’s rule (which is also known as Bernoulli’s rule since Johann Bernoulli also played a part in the solution) to arrive at a limiting value for the two indeterminate forms 0/0 and ∞/∞.
The L’Hopital’s rule says that if f(x) and g(x) are two functions whose individual limits as x tends to some value c, are either both 0 or both ∞, then:
lim xc [f(x)/g(x)] = lim xc [f ’(x)/g ’(x)], provided that the limit exists. In other words, the limit of the division between two functions that both tend to either 0 or ∞, is equal to the same limit of the division between the first derivatives of the two functions; as long is there exists such a limit. This has proven very useful in many mathematical problems, and is widely used in calculus.
If you are studying calculus for WACE exams at higher levels, you will come across limits and indeterminate forms, and will get a chance to apply L’Hopital’s rule. If you have questions about indeterminate forms, you could try to obtain WACE help and ask any online tutor in Australia about it. Most math tutors in Australia would be able to help you with problems related to indeterminate forms.
Find more details about WACE help and professional online tutor Australia from iExel.
Article source: https://articlebiz.comRate article
Article comments
There are no posted comments.
Related articles
- The Impact of Hermeneutical Injustice on ASN Students Involved in Transitions from Early Years Education
- IT TAKES A VILLAGE
- Closing the Digital Gap: Overcoming Accessibility Barriers for Students with Disabilities in Benin City
- Expert Quran Teacher for Kids and Adults
- Why is the study of history is critical?
- First Aid Courses and CPR Training - Safety Learning
- A META-ANALYSIS ON THE IMPACT OF CRAMMING AS LEARNING STRATEGIES AMONG SHS STUDENTS IN GHANA
- Revolutionize Your School's Online Presence with a Cutting-Edge CMS Website Development
- How to Find Emotive Language in a Text: A Comprehensive Guide
- Addressing the Rise of Academic Pressure
- Standard Thickness of Asphalt Pavement
- The Importance of Character Education from an Early Age
- Education, Evolution & AI - Mixing Technology and Learning in the 21st Century
- Obtain Full G Driver’s License in Ontario
- Top Tips for Writing High-Scoring University Assignments Insights from Assignment Experts
- Parents Guide to Finding the Best Bay Area Tutoring for Your Child
- The Ultimate Guide to Choosing the Top Driving School in Manhattan
- Gearing Up: Automatic vs. Manual Driving Lessons
- Unified Field Theory Is Explainable
- Project Management in the Digital Age: Leveraging Technology for Success
- Progressing through the Lean Six Sigma Belt Levels: A Journey from White to Black
- A part of Crisis at school: School violence
- Unlocking Success: Why Phonological Awareness Matters for Kids and How to Support It
- Unlocking the Power of Assessment: Strategies for Effective Evaluation
- Unlocking Intellectual Potential: Edinburgh, UK Manuscript Illustrations
- Viruses, structures, causes and prevention
- the importance of stars
- Love and Limits: How to set limits while preserving loving relationships with students
- Unveiling the Potential: A Comprehensive Exploration of "Crushing It With Crypto 2024: UNLOCKED"
- The Evolution of Artificial Intelligence: Past, Present, and Future