(a) Find the Taylor series for f(x) = ln x centered at x = 1 [3 marks]
(b) Find the Maclaurin series for f(x) = sin x [3 marks]
(c) Find the nth term of the series 1/2 + 2/3 + 3/4 + 4/5 + ...
Using the nth term test, investigate the convergence of the series above. [4 marks]
(d) Investigate the series 1/∑1 + 1/∑2 + 1/∑3 + 1/∑4 + ... for convergence or divergence using the comparison test. [2 marks]
(e) Find the range of values of x for convergence of the series
1/(1 2) + x/(2 3) + x^2/(3 4) + x^3/(4 5) + ... + x^(n-1)/(n(n+1))
[Hint: use Ratio Test] [4 marks]
(f) Find the odd and even parts of the function, f(x) = (1-x)/(1+x). [4 marks]
(g) Given f(x) = 2x^2 - 7x + 10 on ]2,5[, find all values of c in the interval. [3 marks]
(h) Express Z = -4 + 3i in polar form. [3 marks]
(i) Find the modulus and the argument of the complex number Z = ∑5 - 2i. [4 marks]