The function θ (x, t) for x Є [0, 1] and t ≥ 0 is a solution to the heat equation ∂θ/∂t = ∂^ θ/∂x^2 with conditions θ (x,0) = 2 sin πx + 32 sin 27 πx, 0 (θ, t) = 0, and 0 (1, t) = 0. What is 0 (x, A ae at 2 ax2 - In 2)? Note: The answer box will recognize sin, cos, tan, sinh, cosh, etc.; simply put the argument in round parentheses; e.g. sin(pi*x/L). θ (x, 7-2 In 2) = Hint: Note that we actually gave you an answer in terms of the basis for the space variable! That is you have θ (2,0) = u(x) v(0), but you also know a basis for v(t). = All you need to do is multiply by the appropriate time function, and evaluate at the desired value of time!