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# couple of questions for bored buddies out there(functions ,limits,domains..etc) watch

1. got these just want to make suree I've answered them correctly
everybody feel free to help
A-*find the limit if it exist
1)lim(x-->2) [√(x+2) - √(2x)]/ [x²-2x]

2)lim(x--> *negative infinity*) [√(5x²-2)]/(x+3)]

3)lim (x-->3 from the left) [ lx-3l/(x-3)²]

B-eliminatet to find a cartesian equation of the curve, sketch the curve . indicate with an arrow the dircetion in which the curve is traed as t increases

x=cos²t y=cost 0 <=t<=(π/2)
this on I've got a y=√x but i'm not sure, the direction was downwords, and it was reall shrt with coordinates or (1,1) and (0,0)

D-find the domain of
√(X+3)/(lxl+x)

solve for x
[lx²-16l/(x²-x-6)]<=0

I solved all of them but I dont have the key answer, I just wat to make sure I've answered them correctly
2. A 1) -1/8
2) -5
3) -infinity

B) t increases -> cost decrease -> x decrease -> arrow from right to left.

D) Domain: x > 0
x = +/-4
or -2 < x < 3
3. (Original post by BCHL85)

[/B]2) -5 are you sure not -sqrt 5???

3) -infinity
in the end I reached (-1/0) but then I though if it was coming from left then it's 0 from left then I thought if -1/0from left, then minuses cancel and it become +infinity

B) t increases -> cost decrease -> x decrease -> arrow from right to left. yeah and did the caretisian sketch look like y=√x ???,I mean can we subtitute cos²t=x with cos t =√x???

D) Domain: x > 0
x = +/-4
or -2 < x < 3
I wrote x*E (-4,4) - {-2,3} can we do this?
thanx alot by the way
4. yup, I meant to type -rt(5). Sorry
y = rt(x) is right, as cost > 0 for 0 < t < pi/2

You should write x E {-4, 4} U (-2, 3)
as {} for a set of elements, while () for the range , U for union

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Updated: November 12, 2005
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