Question

determine if y={(x^2+2x,x2) is continuous at x=2 worked and explained solutions pleasee!

Answer 1

To check if something is continous first you need to check if it is defined.
Then you need to check the limit as x goes to 2 from left and right.
Finally it is continuous if the function = the limit.

Answer 2

can you help me solving this problem step by step because i have got 4 more exercises of this type and i dont really understand

Answer 3

ok let me start by saying it is not continous. to check if your function is defined you plug in the 2 in the piecewise function.
WHen you plug it into the first piece wise function it =8
when you plug it into the second one you shoud get =-8
because bothg of them do not equal you do not have to go further, you can conclude that it is not defined .
now if they did = then you need to find the limit.

Answer 4

but they did not so it is not continous

Answer 5

I hope that helped!!!

Answer 6

\(y\) is continuous at \(x=2\) if and only if
\[\lim_{x\to2^-}y=\lim_{x\to2^+}y,\]
i.e.,
\[\lim_{x\to2^-}(x^2+2x)=\lim_{x\to2^+}(x^2-6x)\]