Question

Evaluate the limits:
1. as x approaches 1, limit of (x^3 - 1)/(x^2- 1)
2. as x approaches 2, limit of (x^3 - 8)/(2x - 4)

Answer 1

@hartnn

Answer 2

factor \(x-1\) in problem (1) and \(x-2\) in problem (2)

Answer 3

1. how would u do that (x - 1)(x^2 + 1) = x^3 +x -x^2 -1
it does not work

Answer 4

\(x^3-1=(x-1)(x^2+x+1)\)

Answer 5

make use of the factorization of the difference of two cubes
\[a^3-b^3=(a-b)(a^2+ab+b^2)\]

Answer 6

ask, if there are still any doubts....

Answer 7

i wanna try to solve it if u want