why is lim of tanx as x approaches to (pie/2)+ is negative infinity. Shouldnt it be positive infinity since pie/2 is approaching on the right

Answer 1

A quick test using a calculator, find the values of tan(89.99°) and tan(90.01°).

Also, look at the graph of tan(x).

The curve approaches +∞ up to π/2 from the left, and -∞ from the right, which confirms your previous results.