Posted by Joel on October 17, 2002 at 10:01:22:
In Reply to: Limits posted by Rowena Garrison on October 16, 2002 at 23:16:38:
: Here's the question.
: Given the lim f(x)=3, lim g(x)= -2, and g(x)=0.
I assume all of the "given" limits are limits as x approaches a, and you are looking for 2 answers to each question, one with lim g(x)=-2, and one with lim g(x)=0. (Otherwise the question makes no sense). If so, just apply the "limit laws". The limit of a sum is the sum of the limits. The limit of a quotient is the quotient of the limits (provided that the denominator is not zero). The limit of a product is the product of the limits.
Find:
: A. lim as x approaches a of [ f(x) + g(x)] : 3 + (-2) = -0 ; 3 + 0 = 3
: B. lim as x approaches a of [f(x)/g(x)] : 3/(-2) = -(3/2) ; 3/0 is undefined
: C. lim as x approaches a of [f(x)g(x)] : 3*(-2) = -6 ; 3*0=0
: D. lim as x approaches a of [g(x)]^3 : (-2)^3 = -8 ; (0)^3 = 0