Limit of Function And Its Types
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The document discusses different types of limits in calculus and analysis. A limit describes the behavior of a function near a particular input value. There are several types of limits including one-sided limits as x approaches a from the left or right, direct substitution limits where the value is simply substituted, and limits involving techniques like factoring, rationalization, as x approaches infinity, trigonometric functions, or the number e.
Limit of Function And Its Types
- 1. Limit Of Function And Its Types
- 3. In mathematics, the limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular input. Let f be a function defined on some open interval containing a except possibly at a itself. Then, the limit of f as x approaches a is L, written as Limit Of Function lim ( ) x a f x f a
- 4. Limit of f(x) as x approaches a from the Left. Lift Side Limit xf ax lim
- 5. Limit of f(x) as x approaches a from the Right. Right Side Limit xf ax lim
- 6. The limit of f as x approaches -3 exists and it is equal to 0 because Existence OF Limit xf x 3 lim 3 lim 0 x f x 2 9 ( ) 3 x f x x
- 7. Limit By Direct Substitution Limit By Factoring Limit By Rationalization Limit At Infinity Trigonometric Limit Limit Involving Number e Types Of Limit
- 8. These are easiest problems. In these problems you only need to substitute the value to which the independent value is approaching. Direct Substitution
- 9. We use our algebraic skills to simplify the expression Factoring
- 10. In these limits we apply an algebraic technique called rationalization Rationalization
- 11. In these limits the independent variable is approaching infinity At Infinity
- 12. In most limits that involve trigonometric functions you must apply the fundamental limit: Trigonometric
- 13. This types of question have e form Involving Number e
- 14.