Further Maths Homework Due Mon 7th Dec

Total: 30 marks. Show all working out. Those not showing mathematical rigour will be penalised.
A=24, B=21, C=18

1. Find the gradient function for $$y=\frac{x-2}{x^2}$$

   [3 marks]

2. Find the coordinates of any stationary points and determine their nature $$y=\frac{1+x^2}{x}$$

   [5 marks]

3. Find the equations of the tangent and the normal when $x=4$ in the form $ax+by=c$ where a,b and c are integers $$y=\frac{4\sqrt{x}-x^2}{x^{\frac{3}{2}}}$$

   [7 marks]

4. Find $$\int{(x-2)^3} dx$$

   [3 marks]

5. Find $y$ if (1,-2) is a boundary condition $$\frac{dy}{dx}= \frac{x-1}{x^3}$$

   [4 marks]

6. Find $$\int_0^2{(2x-3)^4} dx$$

   [4 marks]

7. Find the area enclosed by the curve $y=1-x^2$ and the x axis

   [4 marks]