Riemann's Sum and Integrals Question

Question

The value of the limit is equal to the area below the graph of a function f(x) on an interval [A,B]. Find f, A, and B. (Do not evaluate the limit).

lim n --> ∞ ∑ni=1 (π)/(6n)tan[(iπ)/(18n)]

I would appreciate any guidance on this question! I thought f(x) would be tan(x/18), A would be pi, and B would be 0.27555, but it is wrong and I'm not sure I am fully understanding the question.

Thank you in advance

Answer 1

Use a right endpoint Riemann Sum with A = 0, B = π/18, and f(x) = 3tanx, then

Δx = (B-A) / n = π/(18n) and x_{i =} πi/(18n)

So, f(x_i)Δx = 3tan(πi/18n)(π/18n) = (π/6n)tan(πi/18n)