Limits
1.0 Introduction
1.1 Basic Method of Evaluation of Limits:
1.2 Questions
1.3 Formal definition of Limit:
1.4 Evaluation of Limits by Direct Substitution Method:
1.5 Neighbourhood Concept:
2.0 Definition of Limit - In a different form:
2.1 One - Sided Limits:
2.2 Left hand Limit of a function:(LHL)
2.3 Right hand Limit of a function:(RHL)
3.0 Conditions for existence of Limit
4.0 Some Standard Limits
5.0 Algebra of limits
6.0 Some Standard Methods of Evaluation of Limits:
7.0 Indeterminate Forms:
7.1 Limits of the form ${1^\infty }$
7.2 Limits of the form ${0^0}$
7.3 Limits of the form ${\infty^0}$
7.4 Limit of a function as $x \to \infty $ :
8.0 Sandwich Theorem / Squeeze Play Theorem:
9.0 L'Hospital's Rule for evaluation of limits:
1.1 Basic Method of Evaluation of Limits:
1.2 Questions
1.3 Formal definition of Limit:
1.4 Evaluation of Limits by Direct Substitution Method:
1.5 Neighbourhood Concept:
2.2 Left hand Limit of a function:(LHL)
2.3 Right hand Limit of a function:(RHL)
7.2 Limits of the form ${0^0}$
7.3 Limits of the form ${\infty^0}$
7.4 Limit of a function as $x \to \infty $ :
If we need to find $\mathop {\lim }\limits_{x \to a} f(x)$.
First choose values of $x$ which are close to $a$, but not necessarily at $a$.
Find corresponding values of $f(x)$ for choosen $x$'s.
We observe as value of $x$ approaches $a$, $f(x)$ value moves closer to certain value. Let that value be $L$.
Then $\mathop {\lim }\limits_{x \to a} f(x) = L$.
Note:
If $f(x)$ value doesn't moves closer to certain value as value of $x$ approaches $a$ instead takes values which varies by large numerical difference, then we say $\mathop {\lim }\limits_{x \to a} f(x) = L$ doesn't exist finitely.
