what is the lim as x approaches 3 of x squared minus 3 divided by 2.?
98350
limit as x tends to 3 ;( x^2 -3)/2 =(3^2 -3)/2 =(9-3)/2 = 3
757452
x=-54\nthis one is incorrect.\ny=-2/3\nx=1\ny=54/2.7\ny=-2 ~
890367
You divide the bottom into the top and then see what happens as the limit of x--> infinity.\n\nso x^3/(x^2-4) = x+4x/(x^2-4). Now notice that when x goes to infinity the second part of our answer is going to 0 because the x^2 part is going to dominate the 4x in the numerator. So when this function gets very large it is going to be closer and closer to y= x +0.\n\nThis is all that is meant by asymptotes. They are the functions that aproximate another function as x reacher infinity or a certain constant where the equation is undefined (0 in the denominator)\n\nhope this helps.
866437
Let one side be 'x', second will be 'x + 5 ' third will be  ( x+5) - 3\nx  + x + 5 + ( x + 5 ) - 3 = 16
854009
lim as x approaches 0 from the positive of (ln x) is negative infinity.\nlim as x approaches 0 from the positive of (sqrt x) is 0.\n\nif the numerator goes to negative infinity and the denominator goes to 0, the limit is negative infinity. it might look like L'hospital's rule is required, but it is not.
1046507
[2x/(x+3)(x-3)]*[(x-3)/4(x)]\ncancelling 2 and x-3 we will get\n=x/(x+3)2(x)\nsimplify we will get\n=x/(2x^2+6x)
790936
x≠０\ncuz if x=0, (x-7)/x^3 is meaningless
949122
isolate the variable.\n\nfirst subtract 3 from both sides.\n2x=6\n\nisolate the variable further.  Divide each side by 2\nx=3
758804
Look at the denominator: e^-6x - 7;  as x gets very large, e^-6x gets very small and soon becomes insignificant with respect to -7, so the limit will be -3/7.
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)
908539
∫ x² = 1/3 * x³ + C\n\nThe value between 1 and 2 is 1/3(2)³ - 1/3(1)³ =\n8/3 - 1/3 = 7/3\n\nNow 3 times this is 3 * 7/3 = 7
831674
1. replace x with -3, calculate and see if you get 0\n2. divide by (x+3) and solve the remaining quadratic equation
884322
(x+2)/(x+2)(x+3)=\n1/x+3
605867
(x^2)/2 - 3(x^(3/2))/(3/2) + c = (x^2)/2 - 2x^(3/2) + c
608336
L'hopital's Rule does not apply in this case as the limit can be evaluated as it is, it is not one of the special cases which you would apply that (infinity / infinity, zero / zero).  Actually, if you did apply L'hopital's Rule, you would get the wrong answer (wrong answer being 1).\n\nIn this case, since as x approaches 3 (from either side), the numerator of the function goes to zero and the denominator goes to some finite, no zero quantity, you can just plug in 3 into the function and evaluate.\n\nThe limit of the function as x --> 3 = 0
749158
The expression you wrote has not limit as x goes to 3. Instead, it grows without bound.\n\nWhat you may have meant to write is the limit of ((x-3)/(x^2-9)).\nFor that expression, both numerator and denominator go to 0 as x goes to 3. So there is a chance that the expression will have a limit.\n\nIt turns out that it does have a limit. In fact, you can find it by first factoring the denominator (x^2 - 9) = (x+3)(x-3), then dividing numerator and denominator by (x-3) (the result is (1/(x+3)), and determining the limit of that expression as x goes to 3 (it equals 1/6).\n\nNote: The first responder (Helmut) gave you the same answer that I did (1/6) by applying l'Hospital's rule. But he did not modify the expression you gave in your question, which I said was required in order to find a limit. But he should not have applied l'Hospital's rule to a a fraction where the denominator goes to 0 at the limit, but the numerator does not. If he had recognized that the numerator has to go to 0, he likely would have done what I did, which is to guess that the numerator should be (x-3), which goes to 0 as x goes to 3. Had he done that, he would have found the same limit (1/6), since d(x-3)/dx = dx/dx = 1.
726112
you distribute the -3/2 to the x and 2 and get 21= -3/2x+3\nsubtract 3\n18=-3/2x\ntimes each side by its reciprocal which would be -2/3\n18x-2/3=-12\nso x= -12