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anonymous
 one year ago
Find the indicated Limit
anonymous
 one year ago
Find the indicated Limit

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freckles
 one year ago
Best ResponseYou've already chosen the best response.3Have you looked at the left and right limit to x=0?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No, I don't understand how this specific example works

freckles
 one year ago
Best ResponseYou've already chosen the best response.3x<0 means to the left of x=0 x>0 means to the right of x=0

freckles
 one year ago
Best ResponseYou've already chosen the best response.3use the functions for x<0 and for x>0 to find the left and right limit

freckles
 one year ago
Best ResponseYou've already chosen the best response.3dw:1433390979523:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, so since there is the x>0 does that mean I use 4x ?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3you use both functions one to find the right limit and one to find the left limit then compare both outputs

freckles
 one year ago
Best ResponseYou've already chosen the best response.3if both outputs are the same then that is what the actual limit is if both outputs are different then the limit does not exist

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0 40  = 4 5(0)  8 = 8 correct? so they are different?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[\lim_{x \rightarrow 0^}f(x)=5(0)8 \text{ here I knew to use } 5x8 \text{ since we have } x<0 \\ \\ \lim_{x \rightarrow 0^+}f(x)=40=4 \text{ I knew to use } 4x \text{ since we have } x>0 \\ \lim_{x \rightarrow 0}f(x) \text{ doesn't exist since left not equal right}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3and yes to your question 4 is not 8

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wow thank you for your help!! for this one, is it 8?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3did you find left and right limit?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3remember we need to look at x>1+ and x>1 x>1+ means look at x>1 x>1 means look at x<1 just as we did before

freckles
 one year ago
Best ResponseYou've already chosen the best response.3except we looked around 0 since we had x approaching 0

anonymous
 one year ago
Best ResponseYou've already chosen the best response.011 = 0 x = 1 = 8 1 + 7 = 8 okay I did them in the order given, but I don't think i did the first one right?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3we are not concerned at what happens at x=1

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[\lim_{x \rightarrow 1^}f(x) \\ \text{ this mean we want to know } f(x) \\ \text{ when} x \text{ approaches } 1 \text { from left }\] the function that occurs directly to the left of the vertical line x=1 is f(x)=1x and we know this because your function tells us to use this function when x<1 so \[\lim_{x \rightarrow 1^}f(x)=11 \] and the the right function to the vertical line x=1 is f(x)=x+7 we know this because your piecewise function says let's use this function when x>1 \[\lim_{x \rightarrow 1^+}f(x)=1+7\] now it looks like you try to find f(1) which is 8 you wouldn't say x=1=8 because that can't be true but this is unnecessary to the problem

freckles
 one year ago
Best ResponseYou've already chosen the best response.3anyways you can conclude since 0 isn't 8 the limit __________?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh alright, Yes the limit does not exist

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thanks so much, these are just hard for me to understand

freckles
 one year ago
Best ResponseYou've already chosen the best response.3like if you want to explain what is hard about it I can try to explain

freckles
 one year ago
Best ResponseYou've already chosen the best response.3or like what you don't get about what I have said

freckles
 one year ago
Best ResponseYou've already chosen the best response.3when evaluating limits we aren't concerned at what happens at x=a but what happens around x=a

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[\lim_{x \rightarrow a^}f(x)\] you see the negative sign that looks like an exponent that tells you want to look directly to the left of x=a and see where the y's are going as x approaches a (From the left)

freckles
 one year ago
Best ResponseYou've already chosen the best response.3dw:1433392350183:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.3dw:1433392388087:dw this is where f is to the left of x=a

freckles
 one year ago
Best ResponseYou've already chosen the best response.3notice the y values are approaches k

freckles
 one year ago
Best ResponseYou've already chosen the best response.3dw:1433392435150:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.3that is the left limit of x=a

freckles
 one year ago
Best ResponseYou've already chosen the best response.3now to the right of x=a you want to use the right piece

freckles
 one year ago
Best ResponseYou've already chosen the best response.3dw:1433392480605:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.3those y values are approaching m

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

freckles
 one year ago
Best ResponseYou've already chosen the best response.3dw:1433392533628:dw if you wanted to know what the left and right limits of x=b were you will see that they are both c

freckles
 one year ago
Best ResponseYou've already chosen the best response.3dw:1433392571595:dw anyways i hope that is more clear
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