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Math Help - Further Maths

  1. #1
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    Further Maths

    1a) Find the set of values of x for which 0 < ( 2 - x - x^2 ) / x^2 < 2

    1b) Find the cordinates of the turning point on the curve y = ( 2 - x - x^2 ) / x2

    2) sketch y = root of (x-2)

    3) Find x such that:
    a) x^4 - 5x^2 6 > 0
    b) | 3 - 2x < or equal to | x + 4 |

    4a) show y = x - 6 is an asymptotoe of the curve y = (x-1)(x-3)/(x+2)

    b) Sketch the curve showing cleanly the other asumptote, the points of intersection of the curve with the co-ordinate axes.

    PLEASE PLEASE PLEASE HELP
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  2. #2
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    Quote Originally Posted by ziad123 View Post
    1a) Find the set of values of x for which 0 < ( 2 - x - x^2 ) / x^2 < 2

    1b) Find the cordinates of the turning point on the curve y = ( 2 - x - x^2 ) / x2

    Mr F says: Solve {\color{red}\frac{dy}{dx} = 0}. You can get dy/dx using either the quotient rule or seeing that {\color{red}y = \frac{2}{x^2} - \frac{x}{x^2} - \frac{x^2}{x^2} = 2 x^{-2} - x^{-1} - 1}.

    2) sketch y = root of (x-2) Mr F says: Upper half of sideways parabola. Vertex at (2, 0).

    3) Find x such that:
    a) x^4 - 5x^2 6 > 0

    Mr F says: Do you mean x^4 - 5x^2 + 6 > 0 or x^4 - 5x^2 - 6 > 0? Either way, I suggest drawing a graph and looking for the values of x for which the graph is above the x-axis.

    b) | 3 - 2x < or equal to | x + 4 | Mr F says: You might start by drawing graphs of y = |3 - 2x| = |2x - 3| and y = |x + 4|. Then find the x-coordinates of the intersection points ....

    4a) show y = x - 6 is an asymptotoe of the curve y = (x-1)(x-3)/(x+2)

    Mr F says: {\color{red} y = \frac{x^2 - 4x + 3}{x+2} = x - 6 + \frac{15}{x+2}} using polynomial long division .....

    b) Sketch the curve showing cleanly the other asumptote, the points of intersection of the curve with the co-ordinate axes. Mr F says: Vertical asymptote x = -2. You should know how to find x- and y-intercepts (especially y-intercept!!).

    PLEASE PLEASE PLEASE HELP
    1a) has been answered here: http://www.mathhelpforum.com/math-he...lp-urgent.html

    It would help if you showed some of your work and said where you were stuck.
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