Develop a finite-difference approximation with T.E. of O(Ay)² for aT/ay at point (i, j) using Tij, Ti,j+1, and T₁+2 when the grid spacing is not uniform.

Compute the gradients of each of the following functions: o = xyz & = ln [(x² - y²)-¹/2] r = || = √√√x² + y² + x² 1/r Note: Remember that your tutorial has Hints in it, at the end of each chapter. If you're stuck, they are often quite useful! • If the answer is a scalar, you can just type it in the box (using the Calcpad if you like, or using / for fractions, ^ for exponents, shift and - for subscripts, etc.) For multiplication, you can either leave a space, or use *. So x*x=xx= x², Note that this is not the same as xx without a space; that will get read as an entirely different variable! • If you need to enter a vector, enter an ordered list of components, so for A you can enter either A = (A₂, Ay, A₂) = {A₂, Ay, A₂}. Note that the system isn't great with multiplying through by overall factors, so it's better not to write e.g. Vo= V = Vr = V= (2A, 2A, 2A₂).

Let z = g(x, y) = x³ + xy² + y² - 6x - 2y +4, where x = r cos (0) and y = r sin(0). Use the chain rule to find 32 at (r, 0) = ( √2, 7). Enter an integer or a fully reduced fraction such as -2, 7, -3/4, 41/7 etc. No spaces please