In the class, we leamt the capital recovery factor (CRF) that is given as i(1+i)n (1+i)n - 1 where i the interest rate and n is the number of annuities received. CRF 4a) (10pts) Given i, find the value of lim CRF n0 4b) (10pts) For a fixed n. find the 1st and 2nd-order derivatives of CRF with respect to i 4c) (5pts) Plot CRF in 3-D space. That is, plot (i.n) along the (x,y) axes while CRF on the z axis. Let i range from 0 to 0.5 at increments of 0.01, and n range from 1 to 30 at increment of 1. You need to show the plot and copy/paste your programming scripts (e.g., Matlab, Python, etc) as part of your solution. In the class, we leamt the capital recovery factor (CRF) that is given as i(1+i)n (1+i)n-1 where i the interest rate and n is the number of annuities received. CRF 4a) (10pts) Given i, find the value of lim CRF n0 4b) (10pts) For a fixed n. find the 1st and 2nd-order derivatives of CRF with respect to i 4c) (5pts) Plot CRF in 3-D space. That is, plot (i.n) along the (x,y) axes while CRF on the z axis. Let i range from 0 to 0.5 at increments of 0.01, and n range from 1 to 30 at increment of 1. You need to show the plot and copy/paste your programming scripts (e.g., Matlab, Python, etc) as part of your solution.