Limits and continuous functions: Recall if a function f is continuous, then limn→[infinity]f(bₙ)=f(limn→[infinity]bₙ) provided limn→[infinity]bₙ exists.(a) Find the limit of aₙ=tan⁻¹(3n/√9n²+4), if it exists.
(b) Can we use this idea to compute limn→[infinity][cos(5/√n)]ⁿ ? Explain why or why not.