The limit is a right-hand or left-hand Riemann sum Σ f(t;)Δt. For t; = πί/n, write the limit as a definite integral. n-1 lim Σ 5 cos( i=0 πίπ n k/? n

Suppose that the sequence x0, x₁, x2... is defined by x0 = 0, x₁ = 7, and xk+2 = xk for k≥0. Find a general formula for xk. Be sure to include parentheses where necessary, e.g. to distinguish 1/(2k) from 1/2k. xk = 0

Let a > 0 and X1 = √a. Define the sequence Xn = √(a + Xn-1), n ≥ 1.Show that (Xn)n is convergent and determine its limit.