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anonymous
 4 years ago
decide if the given function is continuous at the specific value of x...
anonymous
 4 years ago
decide if the given function is continuous at the specific value of x...

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

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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yes it is continuous..

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0it is defined at x=2 right

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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0and 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

anonymous
 4 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: \[f(x)= \frac{ 3x1 }{ 2x6 }\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0the func. is discontinuous when denominator is 0

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.02x6=0 x=3 so, for x=3 the func. is not continuous

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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0it can be any number, no problem with it.. look at its graph http://www.wolframalpha.com/input/?i=plot+ \frac{+3x1+}{+2x6+}

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/input/?i=plot+%283x1%29%2F%282x6+%29

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

anonymous
 4 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 \[x \ge0\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0the 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}}]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/input/?i=piecewise [{{3x2%2Cx%3C0}%2C{x^2%2Bx%2Cx%3E%3D0}}]
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