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anonymous
 one year ago
help please !
to two decimal places, find the value of k that will make the function f(x) continuous everywhere.
anonymous
 one year ago
help please ! to two decimal places, find the value of k that will make the function f(x) continuous everywhere.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1434088494322:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.3evaluate both the left and right limit of x=4

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[\lim_{x \rightarrow 4^}f(x)=? \\ \lim_{x \rightarrow 4^+}f(x)=?\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0my choices are: 11.00 2.47 0.47 none of these

freckles
 one year ago
Best ResponseYou've already chosen the best response.3ok can you evaluate both: \[\lim_{x \rightarrow 4^}f(x)=? \\ \lim_{x \rightarrow 4^+}f(x)=?\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3hint ^ 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

freckles
 one year ago
Best ResponseYou've already chosen the best response.3dw:1434077995749:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.3dw:1434078038396:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.3I don't know. Haven't done the problem.

freckles
 one year ago
Best ResponseYou've already chosen the best response.3would you know how to evaluate: \[\lim_{x \rightarrow 4}(3x+k) \text{ or } \lim_{x \rightarrow 4}(kx^25)\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3Both functions are continuous at x=4 why don't you evaluate the limits by replacing x with 4?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3and you want both (left and right limits of x=4) sides to be equal so you have \[3(4)+k=k(4)^25\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3can you solve linear equations?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Do you have to take a limit here? Can you just substitute 4 for x and set the two parts equal to each other?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3one 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
 one year ago
Best ResponseYou've already chosen the best response.3and informally ( I would say) yes to the second question
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