Problem: To be continuous at x=β1, the value of x2β1x3+1β is taken to be:
Answer Choices:
A. β2
B. 0
C. 23β
D. β
E. β23β
Solution:
x2β1x3+1β=(x+1)(xβ1)(x+1)(x2βx+1)β=xβ1x2βx+1β for xξ =β1
xββ1limβx2β1x3+1β=xββ1limβxβ1x2βx+1β=β23β=β23β
For continuity at x=β1, we must define x2β1x3+1β=β23β.