Indeterminate Forms
An indeterminate form is usually encountered where the limit involves more than one function. It is defined as an expression involving two or more whose limit cannot be determined solely from the individual functions.
The most common indeterminate forms are generated from the limits of ratio of functions,, when both functions evaluate either to 0 or ∞ generating the limits of the form or . Other indeterminate forms include 0 x ∞, ∞ – ∞, 0∞ etc.
Certain algebraic methods can help us avoid these forms.
Determining Limits using Algebraic Manipulation
Limits give us the power to approximate functions and see the values they are approaching. Limit is not the value of the function at a particular point. It is the value which the function is approaching as one moves towards the given point. There are many ways to solve the limits, often limits are easy to solve, but sometimes they evaluate into indeterminate forms which are not defined and are difficult to estimate. The goal is to avoid these forms and solve the limits of the function. Let’s look at some algebraic ways to solve such limits.
Table of Content
- Limits
- Indeterminate Forms
- Limits using Algebraic Manipulation
- Limits by Factoring
- Limits by Rationalization
- Trigonometric limits using Pythagorean Identities
- Double angle Identities
- Sample Problems
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