Limits Question!

Question

 

                 Ax³    if x<2

 F(x)=       7-Ax  if x≥2

 

Find a value of A such that the function f(x) is continuous at the point x=2.

 

A=?

Answer 1

For the function to be continuous at x = 2, the two pieces of the graph must fit together at x = 2.  In other words, Ax³ = 7-Ax when x = 2.

 

So, A(2)³ = 7 - A(2)

 

       8A = 7 - 2A

 

      10A = 7

 

         A = 7/10