Limit Question!!!?

Question

What is the lim as x-->pie/4 of { (sinx-cosx) / [ (cosx)^2 ] }

Answer 1

Since this function is continuous except where cos x=0, and cos (π/4) = √2/2 ≠ 0, we may evaluate this by direct substitution:

[x→π/4]lim (sin x - cos x)/(cos² x) = (sin (π/4) - cos (π/4))/(cos² (π/4)) = (√2/2 - √2/2)/(1/2) = 0