Posted by Ashley on Monday, October 3, 2011 at 7:17pm.
is there a number a such that the lim x>2 6x^2+ax+a+57/x^+x6 exists? if so find the value of a and the limit.

Calculus  Steve, Tuesday, October 4, 2011 at 12:11am
You have a fraction with denominator=0 at x=2
So, you want the numerator to also be zero, or you have no hope of having a limit.
6x^2 + ax + a + 57 = 0
24 + 2a + a + 57 = 0
81 + 3a = 0
a = 27
so,
6x^2  27x + 30 / x^2 + x  6
=(6x15)(x2) / (x+3)(x2)
So, the limit = (6x15)/(x+3) = 3/5
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