PortalOk so this is how you would do limits....
Lim (x^3+8 )/(x^2-4)
x->-2
Lim (√(1+3x^4)-√(1-2x))/(x+x^2+2 x^3 )
x->0
Lim (x^3+8 )/(x^2-4)
x->-2
Lim (√(1+3x^4)-√(1-2x))/(x+x^2+2 x^3 )
x->0
3 posters
Limits
Justice- NH Member
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The first has no limit.
The second is 0 (zero).
The second is 0 (zero).
Justice- NH Member
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So what is a limit? A limit is when a function approaches a certain number. Thus i am asking what happens to the function when (x^3+8 )/(x^2-4) approaches -2.
Thus...
((x)^3+(2)^3)/(x-2)(x+2)
((x+2)(x^2+x+4))/(x-2)(x+2)
(x^2+x+4))/(x-2)
now Plug in -2 and you will get your answer
Thus...
((x)^3+(2)^3)/(x-2)(x+2)
((x+2)(x^2+x+4))/(x-2)(x+2)
(x^2+x+4))/(x-2)
now Plug in -2 and you will get your answer
Ahmed- NH Admin
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So all I had to do was simplify it first?
Justice- NH Member
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Exactly! And it is much faster then making a graph.
Warning: Usually in algebra you CAN NOT divide by variables but since we are doing limits we can
Warning: Usually in algebra you CAN NOT divide by variables but since we are doing limits we can
Ahmed- NH Admin
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Well how do you know if something is not a limit?
Ahmed- NH Admin
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-1.5 is the limit for the first one.
Justice- NH Member
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Every function has a limit. Only if the limit approces infinity it can have no limit. (I need to check though)
And congratz you can plug in numbers!
And congratz you can plug in numbers!
Ahmed- NH Admin
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Wrong! A function is not a limit if it approaches infinity or if it goes in two directions.
Justice- NH Member
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the lim x->0 sin(1/x) is an example cause it has to many wiggles
Ahmed- NH Admin
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No man...forget sin, cos tan. Just use normal ones.
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(√(1+3x^4 )-√(1-2x))/(x+x^2+2 x^3 )*(√(1+3x^4 )+√(1-2x))/(√(1+3x^4 )-√(1-2x)
Simply further
Simply further
Ahmed- NH Admin
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Oh I see...multiplying by the conjugate.
Ahmed- NH Admin
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Lev what book are you using to study AP Cal?
Justice- NH Member
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Im first gona do all of Khan's videos. then i will just do review books.
Ahmed- NH Admin
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Post links to khans videos here
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Ahmed- NH Admin
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Wow...so many vids O.O'!
Doc- NH Member
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tell me when u learn lhospitals rule
Ahmed- NH Admin
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Sure. But could you teach me limits first lol?
Doc- NH Member
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dude i suck at life ... i got a A- in calc
Ahmed- NH Admin
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That's pretty good bro. And limits is the first topic in cal. So...help?
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