Evaluate (x^2) / root (x^3-1) dx   ???
952947
we recongsize that d/dx(x^3) = 3 x^2\n\nso let x^3-1 = t\n\n3x^2 dx = dt\nI am using int for integration sign below\n\n\nso int ( x^2/(x^3-1)^(1/2) dx\n= int( dt/3t^(1/2)\n\n= 1/3 int (dt/t(1/2)) = 1/3 int(t^-(1/2)\n\n1/3 (2 t^(1/2) + C using integral of t^n = t^(n+1)/(n+1)\n= 2/3 (x^3-1)^(1/2) + c
546400
D=square root ((x1-x2)^2 + (y1-y2)^2)
270471
is the question\ny = √x +3\nor y =√(x+3)where both x and 3 are under the root\nFor the first one the domain would be x≥0\nfor the second one the domain would be x≥-3\n\nP.S. The expression under the sqrt cannot be negative.
593331
x + 3 = x (x + 3)\n\nx + 3 = x^2 + 3x\n\nx^2 + 2x = 3\n\nx = 1 or -3
939593
(x^2-x^(3/2))/2x^2 = 1/2-sqrt(x)/2\n        =1/2(1-x^(-1/2))\n\nd(1/2(1-x^(-1/2)))/dx\n=1/2(-(-1/2x^(-3/2))\n= 1/4x^(-3/2)\n\ni hope that this helps
926880
(1+1)-2*3/2^2+2\n\nWithout useing Order of Operations: 2\n\nWith Order of Operations: 2.5
806157
it is \n(x/3x+1/3x)/(3/3x+x/3x)=\n=(x+1)/(x+3)
719816
Round roots??? V(-1) = i
975401
This is an expression not an equation.\n\nSq. root of x = x^1/2\n\nSo sq. root of the sq. root of x = (x^1/2)^1/2\n\nYou can now simplify this using the rule for indices:\n\n(a^m)^n = a^(m*n)\n\nso (x^1/2)^1/2 = x^(1/2*1/2) = x^1/4
1183491
Lim { [ sin(x-1)  ] / [ x^2 + x - 2] }\nx-->1\n\nAdd the following to the denominator\n-2x + 2x +1 -1\n\nLim { [ sin(x-1)  ] / [ x^2 + x - 2 -2x +2x +1 -1] }\nx-->1\n\nLim { [ sin(x-1)  ] / [ x^2 -2x + 1 +3x -3] }\nx-->1\n\nNote: (x^2-2x+1) =(x-1)^2    and  (3x-3) = 3(x-1)\n\nThen\nLim { [ sin(x-1)  ] / [ (x-1)^2 +3(x-1)] }\nx-->1\n\nLim { [ sin(x-1)  ] / [ (x-1)^2 +3(x-1)] }\nx-->1\n\nLim { [ sin(x-1)  ] / [ (x-1)[ (x-1)+3 ] }\nx-->1\n\nLim { [ sin(x-1) / (x-1) ] * [ 1/ (x-1+3 )] }\nx-->1\n\nLet u= x-1 then as x-->1, u--> 0\nand\nLim { [ sin u / u ] * [ 1/ (u+3 )] }\nu-->0\n\nSince\n\nLim  [ sin(u) / (u) ]=1\nu-->0\n\nThen \nLim { [ sin u / u ] * [ 1/ (u+3 )] } = 1 * [1/(0+3)] = 1*1/3 = 1/3\nu-->0
830946
c)\n\n= x^3 + x^2 + x - x^2 - x -1\n= x^3 -1
818643
You asked about the numerator before, didnt you get an answer?\nWith synthetic substitution, you should find that the roots of the numerator are -1, -1, -2, and 3.\nThis gives (x+1)(x+1)(x+2)(x-3)  see *.\n\nAre you sure you typed the denominator correctly?\nYou typed: \nx^6 - 6x^5 + 15x^4 - 30x^3 + 15x^2 - 6x + 1\n(by the way, you need to insert spaces into long polynomials like this one or Yahoo does not display them after 30 spaces.  You can place the mouse cursor over them and see the complete polynomial, but many people dont know that, including the previous answerer.)\nThis is not factorable (over the rational numbers)\n\nHowever, if one digit is changed, namely if -30x^3 was written \n -20x^3, then the denominator becomes a very common one (and one that you may notice just by looking at it if you stay at this factoring stuff for a long time):\nnamely (x-1)^6 !!\n\n\n*\n1st root (-1):\n\n-1 || ..1... 1 ... -7 .. -13 ... -6\n...............-1 .... 0 ..... 7 ..... 6\n————————————\n..........1....0.....-7.....-6... || 0\n\nso (x+1) is a root\n\n2nd root (-1):\n\n-1 || ...1....0.....-7.....-6\n................-1 .... 1 .... 6\n——————————\n..........1...-1 ... -6 .. || 0\n\nso (x+1) is a root again.\n\nx^2 - x - 6 remains\n= (x-3)(x+2)\n\nInteresting correlative problem:\nhttp://answers.yahoo.com/question/index;_ylt=Aqz3W3s3NPcz.j__CQYxK0bsy6IX?qid=20061127003230AA2oHuA
714589
x/(x+3) - 2(x-1)/(x+3)(x+2)\n\nx(x+2) - 2 (x-1)\n--------------------\n   (x+3) (x+2)\n\n\nx^2 +2\n----------\n(x+3)(x+2)
902917
y=1/x^2-3 => y+3 = 1/x^2 => x= +/-sqrt(1/(y+3))
106861
How about:\nx ^2/(x^2-4)+1/(x+2) = 0\nx^2/(x^2-4) = -1/(x+2)\nx^2/(x+2)(x-2) = -1/(x+2)\nx^2/(x-2) = -1\nx^2 = -x + 2\nx^2 + x – 2 = 0\n(x+2)(x-1) = 0\ncan you take it from here?
942305
Okay. You have a few things that you have to consider.\n\nNegative exponents: moves it to the denominator\nFractional exponents: the denominator tells you what the root is, the numerator tells you what the root is rasied to\n\nSo: (x+1)^-2/3 rewritten would be:\n\n1/[cuberoot(x+1)^2]\n\nwhen x is seven you have\n1/[cuberoot(8)^2]\n1/[2^2]\n1/4
768805
Factor out the 3:\n3(x^2+3x+2)\nUnfoil:\n3(x+1)(x+2)\nTake the roots:\nx=-1 or -2