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haterofmath
 2 years ago
Best ResponseYou've already chosen the best response.0\[f(x)= \frac{ 2x4 }{ 3x2 } at x=2\]

helder_edwin
 2 years ago
Best ResponseYou've already chosen the best response.0remember the definition: f is continous at x=a if \[ \large \lim_{x\to a}f(x)=f(a) \]

cinar
 2 years ago
Best ResponseYou've already chosen the best response.1it is defined at x=2 right

cinar
 2 years ago
Best ResponseYou've already chosen the best response.1f(2)=0 \[\large \lim_{x\to 2}f(x)=0=f(2)\]

cinar
 2 years ago
Best ResponseYou've already chosen the best response.1and also this is its graph http://www.wolframalpha.com/input/?i=plot+%282x4%29%2F%283x2%29 as you can see the func. is continuous at x=2, no hole no infinity

haterofmath
 2 years ago
Best ResponseYou've already chosen the best response.0ok. 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: \[f(x)= \frac{ 3x1 }{ 2x6 }\]

cinar
 2 years ago
Best ResponseYou've already chosen the best response.1the func. is discontinuous when denominator is 0

cinar
 2 years ago
Best ResponseYou've already chosen the best response.12x6=0 x=3 so, for x=3 the func. is not continuous

haterofmath
 2 years ago
Best ResponseYou've already chosen the best response.0and what about the numerator?

cinar
 2 years ago
Best ResponseYou've already chosen the best response.1it can be any number, no problem with it.. look at its graph http://www.wolframalpha.com/input/?i=plot+\frac{+3x1+}{+2x6+}

cinar
 2 years ago
Best ResponseYou've already chosen the best response.1http://www.wolframalpha.com/input/?i=plot+%283x1%29%2F%282x6+%29

haterofmath
 2 years ago
Best ResponseYou've already chosen the best response.0ok, so there's only one value of x?

haterofmath
 2 years ago
Best ResponseYou've already chosen the best response.0ok. so how about in this case. f(x) = 3x2 if x<0 x^2+x if \[x \ge0\]

cinar
 2 years ago
Best ResponseYou've already chosen the best response.1the 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+[{{3x2%2Cx%3C0}%2C{x^2%2Bx%2Cx%3E%3D0}}]

cinar
 2 years ago
Best ResponseYou've already chosen the best response.1http://www.wolframalpha.com/input/?i=piecewise[{{3x2%2Cx%3C0}%2C{x^2%2Bx%2Cx%3E%3D0}}]
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