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anonymous
 5 years ago
Check if the function is continuous.
anonymous
 5 years ago
Check if the function is continuous.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[f(x) = \left\{ {{{x^2 + 6x  16} \over {x^2 + x 6}}, x \neq 2} \right\}\] \[{7x  4}, x =2\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I can't order the brackets

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0x^2+x6=(x+3)(x2) x^2+6x16 doesn't have either factor so the limit does not exsit at 3 and 2 so the function is not continuous at either x

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0oh x=2 is defined for 7x4

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0still since the limit doesn't exist at x=2 then f is not continuous there

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeap. sorry for that.

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0all you have to do is make sure the limit exists and the limx>af(x)=f(a) then f is continuous at x=a

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\lim_{x\rightarrow 2}f(x)=\lim_{x\rightarrow 2}\frac{x^2+6x16}{x^2+x6}=\lim_{x\rightarrow 2}\frac{(x+8)(x2)}{(x+3)(x2)}=\lim_{x\rightarrow 2}\frac{x+8}{x+3}=2\] \[f(2)=7\cdot 24=10\] \[\lim_{x\rightarrow 2}f(x)\neq f(2)\Rightarrow f(x)\quad not\enspace continuous\]
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