find the lim x goes to 1- =x^1/(1-x)

Question

just need help evaluating the given limit.

Answer 1

Let δ be a very small positive quantity.

When x=1-δ, x¹/(1-x)=(1-δ)/δ=1/δ-1. As δ→0, 1/δ→∞ (limit approached from the left).

When x=1+δ, x¹/(1-x)=(1+δ)/(-δ)=-1/δ+-1. As δ→0, 1/δ→-∞ (limit approached from the right).

The two limits are dissimilar, so limit as x→1 is indeterminate.

As x→1^- (x approaches 1 from the left, the negative side) the limit is infinity.