lim

Question

x → ∞
tan−1(x7 − x9)

Answer 1

You must have an idea what the tangent function looks like. As Ø approaches 90° or π/2 from the left, tanØ becomes infinitely large positively.
as Ø approaches 90° from the right, it is infinitely negative

now look at (x^7 - x^9), as x --> ∞ , it is hugely negative
thus tan^-1 (hugely negatiave ) approaches 90° or π/2
of course another answer would be -90° or -π/2