Reference no: EM132848130

Problem 1 - Use the ratio a_n+1/a_n to determine if {5ⁿ/2^{n^2}}_n=1^∞ is strictly decreasing, strictly increasing, or neither.

Problem 2 - Determine the convergence or divergence of the sequence with the given n^th term. If the sequence converges, find its limit. If it does not converge, state this.

a_n = In(n²)/2n²

Problem 3 - Set up an integral to find the area given by enclosed by the curve r = 2sinθ + 2 cosθ, where 0 ≤ θ ≤ π. Determine the area of this region (either give an exact answer or a numerical approximation accurate to at least 4 decimal places.)

Problem 4 - Consider the function given by the series

f(x) = _k=0Σ^∞((-1)^kx^2k/2^2k(k!)²).

Determine ∫f(x) dx and specify its interval and radius of convergence.