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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -




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Topic review (newest first)

2006-01-05 02:05:11

Yes, yes, just for exactude.

2006-01-05 01:51:21

True, but in this case, it doesn't matter.  If it approaches negative infinity or infinity from either direction, it is still a vertical tangent.

2006-01-04 21:51:57

It depends of which side you are limiting. If x < -2 and x --> -2 then x+2<0 and 1/(x+2) --> -oo.
If x>-2 and x --> -2 then x+2>0 and 1/(x+2) --> +oo.

2006-01-04 04:21:43

Oy, I completely missed a much more direct way to do the limit:

Since x+2 approaches zero as x approaches -2, x+2 is very close to 0 before it gets there, in other words, very small.  (x+2)^(1/3) then also becomes increasingly small, and multiplying this by 3 has basically no effect as it will also become increasingly small.  So 1 over this means it goes towards infinity.

2006-01-03 20:49:22


2006-01-03 14:33:43

f(x) = abs(x), a corner exists at f(0).  It is literally a corner.

As for the answer, it is D:

For a verticle tangent, the function's slope must approach infinity as it approaches the point.

So what we want is:

Multiplying this by
we get:

Now x+2 approaches 0 as x approaches -2.  But we know that f(x)^(1/3) > f(x) if f(x) < 1.  So the numerator gets (relatively) larger and the denominator gets smaller as x approaches -2.  Therefore the slope approaches infinity, and you have a verticle tangent.

2006-01-03 12:35:36

Yes, it isn't differenciable. And I don't know what is corner, too. Try at

2006-01-03 11:37:56

I just noticed that it isn't differentiable either...

So the only thing i'm unsure of is about the corner

2006-01-03 11:32:47

ok, so my grpah doesn't look like that.. so it doesn't have a cusp, correct?

so, hmm... we aren't sure about A, we aren't sure about B, we know it can't be C, we know it is D, and we know it can't be E..

So we're left with Discussions about A and B..

anything to add on those two?

2006-01-03 11:28:15

For uploading an image direct to the forum use "post reply" or when you've written your quick post, simply edit it. There you can specify the number of images and the path to be uploaded.

2006-01-03 11:23:50

Now it's better.

2006-01-03 11:22:46


2006-01-03 11:22:27

like what? your picture didn't show up sad

2006-01-03 11:15:29

I don't know what is corner, but I think cusp is something like this:
I think (D)

2006-01-03 11:05:42

Which of the following describes the behavior of y = cubicroot(x + 2) at x = -2

(A) differentiable
(B) corner
(C) cusp
(D) vertical tangent
(E) discontinuity

well i graphed the function, and i'm not sure.. i know for sure it isn't E... because f(-2) = 0... it has a value..  uhmm.. as for the rest i'm not sure.. i don't even know what a corner and a cusp is.

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