Mth101

[ahmedakhtarraza]

Question 01:-

Check whether or not the function
is continuous at .


Solution:



f (x) = c

(x2 -9)/x+3 = -3

(x+3)(x-3)/(x+3) =-3

x-3 = -3

x = 3-3 = 0

x = 0

f(0) = (0-9)/ (0+3) = -3 = c

Hence Its Contineous function













Question 02:-

For a function , find the instantaneous rate of change of g(x) with respect to x at a general point .

Solution:

Suppose:
At x0 x = 0


g(0) = (5-0) / (3+0) = 5/3 = 1.6 is rate of change



Question 03:-

By using ( ) definition of the limit of a function, evaluate ‘ ’ corresponding to if ,
.


Solution:

(x2 – 1) / (x + 1)


(x + 1)(x – 1) / (x + 1)

(x – 1)

-1 - 1 = -2

Limit Exist