Compute the surface area of revolution of the given curve

Question

1. Evaluate the integral - ∫3dx/x²(x²+25)

2. Determine whether the improper integral converges, and if so evaluate it-

_-5∫⁴ dx/(x+5)^1/3

3. Calculate the Taylor polynomials T₂(x) and T₃(x) centred at x = a for the given function and value of a.

f(x) = 3tanx, a = π/4.

4. Use the appropriate limit was and theorems to determine the limit of the sequences or state that the sequence dicerges.

b_n = e^2-n2

lim_n→∞ b_n =

5. Compute the surface area of revolution of the given curve about the x-axis over the given interval.

y = 13x², [0, 4].