Friday 4 December 2015

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]

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