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anonymous
 one year ago
help find indicated limits
anonymous
 one year ago
help find indicated limits

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SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\Large\color{slate}{\displaystyle\lim_{x \rightarrow~ 5}f(x)}\) where the function is: \(\LARGE\color{black}{ f(x) = \begin{cases} & x+4,~~~{\large x<5} \\ & 4x,~~~{\large x\ge5} \end{cases} }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1So, for a twosided limit \(\Large\color{slate}{\displaystyle\lim_{x \rightarrow~ 5}f(x)}\) to exist, the limit from the right side and the limit from the left side have to be equal to each other. \(\Large\color{slate}{\displaystyle\lim_{x \rightarrow~ 5^+}f(x)=\lim_{x \rightarrow~ 5^}f(x)}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1What is our function from the left of 5? (when x is less than 5) it is: x+4 and the function from the right side is 4x. So this limit: \(\Large\color{slate}{\displaystyle\lim_{x \rightarrow~ 5^+}f(x)=\lim_{x \rightarrow~ 5^}f(x)}\) would go the following way \(\Large\color{slate}{\displaystyle\lim_{x \rightarrow~ 5^+}(4x) =\lim_{x \rightarrow~ 5^}(x+4) }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1if both sides are not equivalent to each other, then the two sides limit Does Not Exist (DNE). if both sides are equivalent, then this value they are both equal is going to be your answer.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1now, do the substitution directly (plug in 5 for x on both sides)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so it does not exist

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what about the other question?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Yes, from the right side the limit is 9 and from the left side the limit is 1. Does Not exist is correct

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1I need to switch browsers. please wait

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1I will draw something I can't use on this browser now...

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1will do without the pic for now

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Do you see the part of this (piece wise) function that goes from the right to the point where x=3?

princeharryyy
 one year ago
Best ResponseYou've already chosen the best response.0the function is a broken line at point 3, on xaxis with the lines being with different slope and a point at the top the limit simply doesn't exist.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Em, do you see that segment where the line goes from the right to the point x=3?
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