Question

Find a pair of constants a and c such that the function is continuous for all x?



How would I go about this?

Answer 1

This is the function:


\[f(x)= x ^{3}+c \] for x<0



\[ax+c^{2}\] for \[0 \le x <1\]



arctan(x) for \[x\ge1\]

Answer 2

consider the endpoints

Answer 3

x=0 and x=1

Answer 4

you need to set left limit=right limit for x=0
and set left limit=right limit for x=1

Answer 5

\[\lim_{x \rightarrow 0^-}f(x)=\lim_{x \rightarrow 0^+}f(x) \\ \lim_{x \rightarrow 1^-}f(x)=\lim_{x \rightarrow 1^+}f(x) \\ \]