Question

Finding analytically the limit of function f(x)=at x=c at that point

Answer 1

Answer:

chal hat dimag mat ka samja kay

Answer 2

Limit of function

Method of construction

• Consider the function

               $f(x)=\left \{ {{\frac{x^{2}-16 }{x-4},x\neq 4 } \atop {10, x=4}} \right.$

• c=4

Demonstration

1. x   3.9   3.99   3.999   3.9999   3.99999  

      f(x) 7.9   7.99   7.999   7.9999   7.99999

    2. x    4.1   4.01   4.001   4.0001   4.00001

       f(x)  8.1   8.01   8.001   8.0001   8.00001

Observation

• The value of f(x) is approaching to 8 as x→4 from the left.
• The value of f(x) is approaching to 8 as x→4 from the right.

• So, $\lim_{x \to \44^{-} } f(x)=8$ and $\lim_{x \to \44^{+} } f(x)=8$

• $\lim_{x \to \44^{-} } f(x)= \lim_{x \to \44^{+} } f(x)$

Result

$\lim_{x \to \44 } f(x)=8$  but function is not continuous.

Application

This activity is useful in understanding the concept of limit and continuity of a function.