limits ;(

[mathishardd]

I don't get how you find the values of parameter c

 

[lev888]

Do you understand all the terms? In the first problem where can the function be discontinuous?

 

[HallsofIvy]

All polynomials are continuous for all x. A "piecewise" polynomial can be discontinuous only at the "joins"- where the polynomial formula changes. It will be continuous if and only if the two "pieces" have the same value at such a point. For example, if \(\displaystyle f(x)= x^2\) for \(\displaystyle x\le 1\) and \(\displaystyle f(x)= x^3+ ax+ 3\) for \(\displaystyle x> 1\), I know immediately that f is continuous for all x except, possibly, x= 1. At x= 1 the two "pieces" evaluate to \(\displaystyle 1^2= 1\) and \(\displaystyle 1^3+ a+ 3= 4+ a\). In order that f be continuous at x= 1, and so for all x, we must have 4+ a= 1 or a= -3.