Answer Happy

I need help with this please and need it asap if possible.
df(a) dc dc2 This homework deals with approximations for the function f(x) = (1+x)" which will be useful in studying tides. 1) A Taylor series approximation to f(x) about x = O is f(x) = f(0) + f'(0)x + 3 f"(O)22+... where df(x) df(x) f'(x) = and f'(0) = da"\r=o. Similarly, f"(x) = etc. Show that f(x) = (1+x)" =1+nx + in(n − 1)x² +.... (See the solutions for help.) 2) Consider x = 0.05. Compute (1 + x)" with this x for n = 1, 2, 5, and 10. Compare to 1+ nx for the same values. Compare to 1+na+žn(n − 1)22 for the same values. 3) Repeat 2) but for n = -1, -2, and -3. 4) Now consider the following financial thoughts. Suppose you get an investment return i per year (interest). If you invest an amount P, after one year, you will have P(1+i). After 2 years you will have P(1+i)2. After N years, you will have P(1+i)”. Suppose you put P = $2000 in the stock market at the beginning of your working career and that i=0.07 (a reasonable long-term stock market return) for the N = 35 years you work. How much will that initial investment be worth at the end? Use an exact calculation. 5) If you put in P every year and you get i return per year, you will have a total T = ? [(1+i)N+1 – 1) at the end of N years. How much will you have if P = $2000, i = 0.07, and N = 35? Again, use an exact calculation. My advice is to set up an IRA or other retirement plan as soon as you can and put as much as you are able to into it early. You will be glad you did.