How to find Intervals of continuity? pls help!

Question

anonymous · Answer

attachment

anonymous · Answer

Image isn't working, try again and I'll see if I can help.

anonymous · Answer

for a. ) i equated both of the equation and got $$1\neq0$$
so it is not continuous

b.) $$\lim_{x \rightarrow 0-}x^3+4x+1= 1\neq \lim_{x \rightarrow 0+} 2x^3=0$$
thus it is not continuous in left or right

c. im not sure what the question menas

anonymous · Answer

*means

anonymous · Answer

@Helloimjohn1234 , i hve uploaded the qn alr(:

anonymous · Answer

I'm not quite sure what they mean in question a). That piece-wise function is continuous everywhere based on the given bounds. Part b) just wants to know if the continuity is conditional, not necessarily that their limits are equal. Because f(x) is continuous from the left and from the right at zero, we can say that it is continuous everywhere. Just my .02

anonymous · Answer

omg that makes sense! okay part a, i did lim x->0 for 1st piece-wise, and i get 1, same goes for the 2nd piecewise, i get 0, isnt that enough to prove its not continuous?