#AP Calculus Limitations

24 messages · Page 1 of 1 (latest)

compact lagoon
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None of the lines are approaching 4, correct

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But the limit says x is approaching 4

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When x is approaching 4, your limit will be what x is at 4

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Not what y is

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It does

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The question is what is y approaching as x approaches 4

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Yup, but sometimes you need to use limit definition

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It's mostly what y is there, but in some cases it can be different

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You know when you have a closed dot, and an open dot what the real y value is right ?

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Look at x = 2

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You have 2 open dots and 1 closes dot

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Yes, y=1 is closed dot, y = 0,2 are open dots

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Closed dot is what the real value at that position is

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Open dots are what it would have been if we continued the graph

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So if we take x-->2+

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X approaches 2 from positive side

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The real value of y at 2 is 1 right ?

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But is the graph approaching 1 ?

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Yup

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Aha good job

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Tell me when you learn derivatives, Imma tell you a cool thing about limits

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You are welcome

charred sage
sage surge
# charred sage

a) f(g(x)) = (2x + 1) + 4 = 2x + 5
b) g(f(x)) = 2(x + 4) + 1 = 2x + 9
c) f(g(-1)) = 2(-1) + 5 = 3
d) g(f(-1)) = 2(-1) + 9 = 7