Is 2x^2+3x continuous?

Question

solomonzelman · Answer

It' has no restrictions for the domain.

perl · Answer

short answer or long answer ?

solomonzelman · Answer

And if the domain can be any (real) number, then is it continuous or not?

perl · Answer

short answer = yes

perl · Answer

long answer , polynomials are continuous (this can be proven)

anonymous · Answer

I just know that the limit is 5 and i didn't know if that had anything to do with it or not.

perl · Answer

as x approaches 1, the limit is 5

solomonzelman · Answer

For a function to be continuous. you have to have:
$$\large\color{blue}{   \lim_{x \rightarrow c} f(c)~~~\rm{exi sts}  }$$for any real number c.


$$\large\color{green}{   \lim_{x \rightarrow c} f(x)~~~\rm{exi sts}  }$$basically saying that,$$\large\color{green}{   \lim_{x \rightarrow c^+} f(x)=\lim_{x \rightarrow c^-} f(x)  }$$

$$An d,~~~\large\color{red}{   \lim_{x \rightarrow c} f(x)=f(c)  }$$

solomonzelman · Answer

These are 3 conditions.

anonymous · Answer

So then it would be continuous at x=1.  Because a x=1 it's limit is 5?

solomonzelman · Answer

yes. it is continua for x=1, and for any other x-value.

solomonzelman · Answer

continuous*  for x=1....

anonymous · Answer

Okay thank you!

solomonzelman · Answer

you welcome