anonymous
  • anonymous
if x approaching 3 from the left =22 and x approaching 3 from the right = 22 but the lim f(x) as x approaches 3 = 20. is the function continuous at x=3? why or why not
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
? if the limit from the left is 22 and the limit from the right is 22, then the "limit' cannot be 20
anonymous
  • anonymous
im given a piecewise
anonymous
  • anonymous
f(x)= 2x^2 +4 when x<3 20 when x=3 28-2x when x>3

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anonymous
  • anonymous
and im asked to find the limit of x to 3+ x to 3- x to 3
anonymous
  • anonymous
piecwise or not, if \[\lim_{x\rightarrow 3^-}f(x)=22=\lim_{x \rightarrow 3^+}f(x)\] then the limit is 22, not something else
UnkleRhaukus
  • UnkleRhaukus
the function is not continuous at the point x=3
anonymous
  • anonymous
ah the limit is 22, but the function is not continuous at 3 because it is not the same as the value of the limit there
anonymous
  • anonymous
why is that unklerhaukus
anonymous
  • anonymous
for the function to be continuous, it must have the same value as the limit
anonymous
  • anonymous
so since \[\lim_{x\rightarrow 3} f(x)=22\] but \[f(3)=20\] it is not continuous at 3
anonymous
  • anonymous
ok
UnkleRhaukus
  • UnkleRhaukus
Satellite73 has already said this but The function is Only continuous at some point if the limit Exists And is Equal to the function at that point.
anonymous
  • anonymous
ok can you help me with this one state the definition of a function f(x) which is continuous at x= a
anonymous
  • anonymous
Yes, actually this (following) statement is pretty confusing "the lim f(x) as x approaches 3 = 20."
anonymous
  • anonymous
i was wrong there
anonymous
  • anonymous
A function is continuous at x=a if \[ \large \space \lim \limits_{x\rightarrow a^-}f(x)=f(a)=\lim \limits_{x \rightarrow a^+}f(x) \]
UnkleRhaukus
  • UnkleRhaukus
(assuming the limit exists of course)
anonymous
  • anonymous
If \( \space \lim \limits_{x\rightarrow a^-}f(x)=\lim \limits_{x \rightarrow a^+}f(x) \) then the limit exists.

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