Mathematics

Session Functions, Limits and Continuity - 2

Session Objectives  Sandwich Theorem  Limits of Trigonometric Functions  Limits of Exponential Functions  Limits of Logarithmic Functions  Limit at Infinity

Theorem Note: If f(x)<g(x) for all x, then we can not say that. If f and g are real functions defined in an open interval containing a such that and both exist. Then,

Sandwich Theorem Let f, g, h be real functions defined in an open interval containing ‘a’ such that in the neighborhood of ‘a’

Limits of Trigonometric Functions

Example-1(i) Solution :

Example-1(ii) Solution :

Example-1(iii) Solution :

Solution Cont.

Example-1(iv) Solution :

Solution Cont.

Example-1(v) Solution :

Example-1(vi) Solution :

Solution Cont.

Limits of Exponential Functions

Limits of Exponential Functions (Cont.)

Limits of Logarithmic Functions

Example-2(i) Solution :

Solution Cont.

Example-2(ii) Solution :

Solution Cont.

Example-2(iii) Solution :

Solution Cont.

Example -2 (iv) Solution :

Solution Cont.

Solution-2 (v) Solution :

Solution Cont.

Thank you