I need help on calc 2

Question

find limits 

 

  lim

x->2^-      tan^-1(1/4-x^2)

Answer 1

As x → 2^-, 4-x²→0⁺.  So, 1/(4-x²) → ∞

 

Therefore, lim_(x→2^-) [Tan^-1(1/(4-x²))] = Tan^-1(∞) = π/2

Answer 2

What happens to the values of  tan^-1(1/4 - x²) as it approaches x=2 from the left?  Do they increase or decrease?

 

In order to figure this out, you need to first find the vertical asymptotes of this function to get a reference base point.  Then use the vertical asymptotes to evaluate the function at x values close to 2, but before it.