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Section A Answer the following three questions. Question 1 carries 10 marks, both question 2 and 3 carry 15 marks. 1. Find the Mclaurin series of the function f(z) = log (z +1), showing clearly the pattern that emerges in the coefficients and the resulting series. 2. The function f is given by the equation f(z) = (2+1)ez Answer the following three question parts. (a) Find the first derivative of the function and so find a simple differential equation satisfied by the function. From these results, write down the McLaurin coefficients a, and aj. (b) Find the first few derivatives of the function f using this differential equa- tion. (c) Use the result of the previous question to find an expression for the remain- ing McLaurin coefficients for the function f. Use this result to produce the general term of the McLaurin series for the function. Explain how the an- swer may be checked