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Tangent ProblemIts givin me a really really bad headache

  1. Dec 7, 2004 #1
    the curve with the equation y=e^x/2 meets the y axis at point A

    a)Find the equation of tangent
    This is easy as pie..I have got the equation as 2y=x+1

    b)The point B has the x co-ordinate ln4 and lies on the curve.The normal at B to the curve meets the tangent at A to the curve at the point C.
    provr that x co ordinate of C is 3/2+ ln 2 and find the y co ordinate of C
    >>>>This question is really killing me ...Any help would really be appriciated

    c)Find in terms of e,the area of the finite region bounded by the curve with the equation y=1/2 e^x,the co ordinate axis and the line with the equation x+2=0
    >>>>this looks easy..just gimme some hint please
  2. jcsd
  3. Dec 8, 2004 #2
    b) Find the (x, y) coordinates of A and B (at A x=0 and at B x=ln4). Find the equation of the normal to the curve at B (the slope of the normal is (1/y'), where y is the equation of the curve). The normal at B and the tangent at A intersect at point C; what does that tell you about C?

    c) Draw a sketch of y=0.5ex and x=-2. Where does the line x=-2 intersect the curve? Where does the curve intersect the y-axis? (The answers to these are the bounds of the integral that gives you the area.)
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