Limits
Chapter Name : Limits And Derivatives |
Sub Topic Code : 104_11_13_03_03 |
Topic Name : Limits |
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Sub Topic Name : Limits Of Polynomials And Rational Functions |
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Introduction
• Sometimes we cannot work something directly for a function. We want a closer and closer value for that function. We call that Limit of a function. • Limits looks at what happens to a certain function when value approaches a certain value. • In this section we apply limits to polynomials and rational functions.
Pre-Requisites:
• Knowledge of Polynomials, Rational Functions. • Knowledge of limits.
Activity:
Observe what significance these limits have.
Real Life Question:
A mobile company charges 1$ for first one minute (or part of a minute) and additional 0.50$ for additional minute (or part of a minute). What significance limits have for this problem?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Limit of function | Limit of a function investigates the behavior of function as the value of variable in function approaches closer and closer to some constant. |
| Polynomial | An expression constructed of variables and constants being added, Subtracted, multiplied and divided and where the terms have non-negative exponents. |
| Rational function | A function is rational if it can be written as ratio of two polynomials. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Cell phone | Note the charges for the first minute and also additional charges for additional minute. Write a polynomial for this function. Apply limits for a t->4. |
Real life uses :
Limits and polynomials are used in financial statistics.
Practical examples around us
| Examples | Explainations |
|---|---|
| Speed of car | If velocity of car is constant we can find velocity of car by finding change in distance by change in time. If the velocity of car is not constant throughout the time frame involved then how to find the velocity at different points? We can find velocity of car at different points by applying limits concept as the car moves closer to point of interest. |
What you learn in Theory:
For any polynomial function P(x), lim?(x?a)??P(x)? = P(a). For rational polynomial function, lim?(x?a)??P(x)= ? lim?(x?a)??g(x)/h(x)?=(g(a))/(h(a))
What you learn in Practice:
When we consider limits we are considering the behavior of a given function as it approaches closer and closer to given point.