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haterofmath
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decide if the given function is continuous at the specific value of x...
 2 years ago
 2 years ago
haterofmath Group Title
decide if the given function is continuous at the specific value of x...
 2 years ago
 2 years ago

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

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

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

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

cinar Group TitleBest ResponseYou've already chosen the best response.1
f(2)=0 \[\large \lim_{x\to 2}f(x)=0=f(2)\]
 2 years 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
 2 years 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: \[f(x)= \frac{ 3x1 }{ 2x6 }\]
 2 years ago

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

haterofmath Group TitleBest ResponseYou've already chosen the best response.0
and what about the numerator?
 2 years 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+}
 2 years ago

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

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

cinar Group TitleBest ResponseYou've already chosen the best response.1
in this case yes..
 2 years 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 \[x \ge0\]
 2 years 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}}]
 2 years 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}}]
 2 years ago
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