(i) Given that f ( x ) =5 x 2 +10 x + k and f (0) =100, find the value of k and evaluate f ( ) (2…
(i) Given that f(x) =5x2 +10x+kand f(0) =100, find the value of kand evaluate f()(2 marks)
x3+ x2-9x-9
(ii) The function f(x)=x2–9does not exist for two numbers of the real line. Find these two numbers of the real line and define f(x)at each of these points, so that it becomes a continuous function. (4 marks)
(b). Compute the following limits
x3-5x2+2x-4
(i) xlim?2 x2–3x+3 (3 marks)
4x2+x+1
(ii) lim?83x2+2x+5 (3 marks)x
(c). (i) Distinguish between an annuity due and an immediate annuity giving an example for each.
(4 marks)
(ii) A man pays a premium of 100 at the beginning of every year to an insurance Company on the understanding that at the end of fifteen years he can receive back the premiums which he has paid with 5% compound interest. Calculate the amount of money he should receive. Give your answer correct to three significant figures. (4 marks)
