Further Mathematics 7366: Further Calculus Topical Past Paper Questions

The function f is defined by $$ \mathrm{f}(x)=\frac{1}{\sqrt{x}}\quad4\leq x\leq7 $$ Find the mean value of f over the interval $ 4 \leq x \leq 7 $ Give your answer in exact form.

a) Find and simplify the first five terms in the Maclaurin series for $ e^{2x} $ [2 marks] Hence, or otherwise, write down the first five terms in the Maclaurin series for $ e^{-2x} $ [1 mark] (c) Hence, or otherwise, show that the Maclaurin series for $ \cosh(2x) $ is $ a + bx^{…

The function f is defined by $$ \mathrm{f}(x)=\frac{x^{2}-3}{x^{2}+px+7}\quad x\in\mathbb{R} $$ where $p$ is a constant. (a) The graph of $y = f(x)$ has only one asymptote. Write down the equation of the asymptote. [1 mark] Find the set of possible values of $ p $ [4 marks] Find…