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:
1.4 Evaluation of Limits by Direct Substitution Method:
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 $ :
Question 3.
If $f(x) = {x^2} + 3$.
Find $\mathop {\lim }\limits_{x \to \sqrt 3 } f(x)$.
Solution:
$\mathop {\lim }\limits_{x \to \sqrt 3 } f(x) = \mathop {\lim }\limits_{x \to \sqrt 3 } {x^2} + 3$
$ = {\left( {\sqrt 3 } \right)^2} + 3$
$ = 3 + 3$
$ = 6$
Question 4:
Find $\mathop {\lim }\limits_{x \to 0} \cos x$.
Solution:
$\mathop {\lim }\limits_{x \to 0} \cos x = \mathop \cos (0)$
$ = 1$