for what value of the constant c is the function f continious

Question

For what value of the constant c is the function f continuous on (-infinity,+infinity) where

f(s)= {s²-c         if s ξ(-infinity,8)

        {cs+4        if s ξ[8,infinity)

c=

 

Answer 1

Set s to a tiny bit less than 8 and evaluate the top expression, also set s = 8 and evaluate the bottom expression:

 

8^- 2  - c   and c(8) + 4 

 

As s approaches 8 these must become equal so:

 

64^- - c = 8c + 4

 

Combine like terms:

 

60 = 9c => c = 60/9 or 6 2/3

 

Check at 8:

 

64 - 6 2/3 = 57 1/3

 

6 2/3 (8) + 4 = 57 1/3   √