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

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

cinar Group TitleBest ResponseYou've already chosen the best response.1
yes it is continuous..
 one year ago

cinar Group TitleBest ResponseYou've already chosen the best response.1
it is defined at x=2 right
 one year ago

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

cinar Group TitleBest ResponseYou've already chosen the best response.1
and 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
 one year ago

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

cinar Group TitleBest ResponseYou've already chosen the best response.1
the func. is discontinuous when denominator is 0
 one year ago

cinar Group TitleBest ResponseYou've already chosen the best response.1
2x6=0 x=3 so, for x=3 the func. is not continuous
 one year ago

haterofmath Group TitleBest ResponseYou've already chosen the best response.0
and what about the numerator?
 one year ago

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

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

haterofmath Group TitleBest ResponseYou've already chosen the best response.0
ok, so there's only one value of x?
 one year ago

cinar Group TitleBest ResponseYou've already chosen the best response.1
in this case yes..
 one year ago

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

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

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