Problem: To be continuous at x=−1, the value of x2−1x3+1​ is taken to be:
Answer Choices:
A. −2
B. 0
C. 23​
D. ∞
E. −23​
Solution:
x2−1x3+1​=(x+1)(x−1)(x+1)(x2−x+1)​=x−1x2−x+1​ for xî€ =−1
x→−1lim​x2−1x3+1​=x→−1lim​x−1x2−x+1​=−23​=−23​
For continuity at x=−1, we must define x2−1x3+1​=−23​.