Question

lim x=1 ax2+bx+c/cx2+bx+a

Answer 1

The limit of the given expression depends on the values of a, b, and c.

1. If a+b+c ≠ 0, the limit is 1.
2. If a+b+c = 0 and a ≠ c, the limit is -1.
3. If a+b+c = 0 and a=c (which implies b=-2a and a ≠ 0), the limit is 1.

Answer 2

The problem requires evaluating the limit of a rational function as x approaches 1. Direct substitution leads to different cases based on the value of a+b+c. If a+b+c is not zero, the limit is 1. If a+b+c is zero, L'Hopital's Rule or factorization is applied, leading to further sub-cases where the limit can be -1 or 1, depending on whether a equals c.