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## haterofmath Group Title decide if the given function is continuous at the specific value of x... one year ago one year ago

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1. haterofmath Group Title

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

2. helder_edwin Group Title

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

3. cinar Group Title

yes it is continuous..

4. cinar Group Title

it is defined at x=2 right

5. cinar Group Title

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

6. cinar Group Title

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 Group Title

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 Group Title

the func. is discontinuous when denominator is 0

9. cinar Group Title

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

10. haterofmath Group Title

and what about the numerator?

11. cinar Group Title

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 Group Title
13. haterofmath Group Title

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

14. cinar Group Title

in this case yes..

15. haterofmath Group Title

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

16. cinar Group Title

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 Group Title

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