anonymous
  • anonymous
help please ! to two decimal places, find the value of k that will make the function f(x) continuous everywhere.
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
|dw:1434088494322:dw|
freckles
  • freckles
evaluate both the left and right limit of x=4
freckles
  • freckles
\[\lim_{x \rightarrow 4^-}f(x)=? \\ \lim_{x \rightarrow 4^+}f(x)=?\]

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More answers

freckles
  • freckles
oops -4
anonymous
  • anonymous
my choices are: 11.00 -2.47 -0.47 none of these
freckles
  • freckles
ok can you evaluate both: \[\lim_{x \rightarrow -4^-}f(x)=? \\ \lim_{x \rightarrow -4^+}f(x)=?\]
freckles
  • freckles
hint ^- means look to the left (which is the left function of x=-4 and use it to plug in -4 into) hint ^+ means look to the right (which is the right function of x=-4 and use it to plug in -4 into) both the left and right limit need to be equal so that you can have the actual limit at x=-4 exist
anonymous
  • anonymous
o.o im lost lol
freckles
  • freckles
|dw:1434077995749:dw|
freckles
  • freckles
|dw:1434078038396:dw|
anonymous
  • anonymous
is it A?
freckles
  • freckles
I don't know. Haven't done the problem.
freckles
  • freckles
would you know how to evaluate: \[\lim_{x \rightarrow -4}(3x+k) \text{ or } \lim_{x \rightarrow -4}(kx^2-5)\]
anonymous
  • anonymous
no. o.o
freckles
  • freckles
Both functions are continuous at x=-4 why don't you evaluate the limits by replacing x with -4?
freckles
  • freckles
and you want both (left and right limits of x=-4) sides to be equal so you have \[3(-4)+k=k(-4)^2-5\]
freckles
  • freckles
can you solve linear equations?
anonymous
  • anonymous
Do you have to take a limit here? Can you just substitute -4 for x and set the two parts equal to each other?
freckles
  • freckles
one of the things we need for continuity at x=-4 is: \[\lim_{x \rightarrow -4}f(x)=L\] we get to have this if : \[\lim_{x \rightarrow -4^{-} }f(x)=\lim_{x \rightarrow -4^{+}}f(x)=L\] so formally the answer is yes to that question
freckles
  • freckles
to the limit one
freckles
  • freckles
and informally ( I would say) yes to the second question

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