Limits
A limit is a value the function or a sequence approach as the input or the index approaches some value. These concepts are essential in calculus and real analysis as they help us define continuity, differentiability, and integrals. In the formula, the limit for a function f(x) at a point x = c is usually denoted as,
Often only the substitution method is enough for calculating the limit. But sometimes some limits might evaluate to indeterminate 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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