## haterofmath 3 years ago decide if the given function is continuous at the specific value of x...

1. haterofmath

$f(x)= \frac{ 2x-4 }{ 3x-2 } at x=2$

2. helder_edwin

remember the definition: f is continous at x=a if $\large \lim_{x\to a}f(x)=f(a)$

3. cinar

yes it is continuous..

4. cinar

it is defined at x=2 right

5. cinar

f(2)=0 $\large \lim_{x\to 2}f(x)=0=f(2)$

6. cinar

and also this is its graph http://www.wolframalpha.com/input/?i=plot+%282x-4%29%2F%283x-2%29 as you can see the func. is continuous at x=2, no hole no infinity

7. haterofmath

ok. so if they were ask to list all the value of x for which the given function is not continuous...how would that work? Example: $f(x)= \frac{ 3x-1 }{ 2x-6 }$

8. cinar

the func. is discontinuous when denominator is 0

9. cinar

2x-6=0 x=3 so, for x=3 the func. is not continuous

10. haterofmath

11. cinar

it can be any number, no problem with it.. look at its graph http://www.wolframalpha.com/input/?i=plot+ \frac{+3x-1+}{+2x-6+}

12. cinar
13. haterofmath

ok, so there's only one value of x?

14. cinar

in this case yes..

15. haterofmath

ok. so how about in this case. f(x) = 3x-2 if x<0 x^2+x if $x \ge0$

16. cinar

the func. is not continuous at x=0 why because limit does not exists when we approach to 0, from left limit is -2, from right limit is 0 http://www.wolframalpha.com/input/?i=piecewise+ [{{3x-2%2Cx%3C0}%2C{x^2%2Bx%2Cx%3E%3D0}}]

17. cinar

http://www.wolframalpha.com/input/?i=piecewise [{{3x-2%2Cx%3C0}%2C{x^2%2Bx%2Cx%3E%3D0}}]