1. The problem statement, all variables and given/known data The figure shows a heavy weight suspended by a cable and pulled to one side by a force F. We want to know how much force F is required to hold the weight in equilibrium at a given distance x to one side (say to place a cornerstone correctly). From elementary physics, T cos θ = W , and T sin θ = F . (a) Find F/W as a series of powers of θ. (b) Usually in a problem like this, what we know is not θ, but x and l in the diagram. Find F/W as a series of powers of x/l. 2. Relevant equations Tcos(theta) = W Tsin(theta) = F sin(theta) = (x/l) cos(theta) = sqrt(l^2-x^2) = sqrt(1-(x/l)^2)[/B] 3. The attempt at a solution The first part was a relatively simple solve, it was just a power series of the tangent function. The second part is what I am stuck on. I have (F/W) = (x/l)(1/sqrt(1-(x/l)^2)), but I have no clue how to turn the right side of this equation into a power series. Should I just create 2 different functions (one where x is a function of l and another where l is a function of x) and write 2 power series, or is there a way that I am not seeing? I have also tried just letting theta = arcsin(x/l) and substituting that into the power series I found in part 1, but that solution was incorrect. I am at a complete loss. Any help would be much appreciated. Thanks in advance!