posted by soasi piutau .
1) find the indicated limit, if it exist?
a) lim x->-2 (x^2 -9)/(x^2+x-2)
b) lim x -> -∞ √(ax^2+bx+c)/dx + e, where a > 0, b,c,d, and e are constant.
since you have (x-3)(x+3) / (x-1)(x+2) the numerator is nonzero when x = -2, the limit will be ±∞, depending on the direction of approach,
I assume you meant √(ax^2+bx+c)/(dx+e) since otherwise it is boring. Divide top and bottom by x to get
√(a+b/x+c/x^2)/(d+e/x) = √a/d
however, the numerator is positive and the denominator is negative as x -> -∞, so we really end up with -√a/d