Asheesh's Web Page

I'm Asheesh, as my title suggests. I go to Troy Athens High School as a freshman =( . I have several hobbies which include, playing tennis =), soccer, and watching T.V. Mr.Block is my second hour teacher, and this is my webpage, devoted to Calculus.

 
Answers to the 2003 Free Response Questions

1a. The area of region R is determined by: the intergal of the top curve, - the intergal of the negative curve, from the limits of A to B where A is the intersection which equals .239, and B is given to be 1. All you have to do is solve the equation of : the integral from .239 to 1 of (x^(.5))-(e^(-3x)) which equals .443 units square.

1b. Washer method: pi r^2 - pi * integral from .239 to 1 of ((1 - e^(-3x))^2)-(1 - x^(.5)^2) the answer would be 1.424 cubic units.

1c. This is confusing to understand - but one does this by integrating the cross section from .239 to 1: (5)(x^(.5) - e^(-3x))^2 therefore the answer is equal to 1.554 cubic units.

2a. dy/dt is negative, altitude is decreasing as time increases and dx/dt is also decreasing as the particle is moving to the left side.

2b. It is undefined when dx/dt = 0. So solve the equation which i don't feel like writng out and you get the value 3, so at time equals three, point B is undefined for it is a cusp.

2c. The velocity vector is determined by finding x and y prime at t = 8, given, and when all is calculated you get (-4.5, 2.5) at t = 8. Speed integral of the square root of dy/dt squared + dx/dt squared, which is equal to 5.148

3a. 5/3y = squareroot of 1+y^2 there fore you get P is (1.25, .75) For the curve C(I don't feel like writing out) At point P where y = .75, this equals .60

3b. Area of region S = the integral from 0 to .75 of (the square root of (1+y^2)-5/3y) Areai is = to .347, Use calculator

3c. x^2 - y^2= 1, let x = rcos theta and y = rsin theta, so r^2cos^2theta- r^2sin^2 = 1 blah blah, just simplify and u get the right answer.

  • Donut
    • This website is about the volume of the donut box using the aid of derivatives, and the volume of sweet yummy donuts!
  • Volume of a Vase
    •  This is explanatory, one has to find the area of the vase by graphing the points and putting it into a logistic equation.
  • Curve length
    • This is pretty straight forward you have to find the area of different curves using the formula ((dy/dx)^2 + (dy/dt)^2)^.5
  • Area under curve
    • Using Riemann Sums you have to calculate the area of differnt curves, this is relatively easy
  • Curve Fitting
    • This website shows the best way to graph a curve and fit the points one has to plot
  • Taylor Series
    • This is the Taylor polynomial page and just talks about how to solve them and stuff
  • Equation of a Circle
    • This website is playing around with the equation of a circle and its graph.

    Good sites to visit.
  • Mr. Block's Web Page
  • ESPN
  • Athens
  • MiniMafia
  • Pei's Site

    •  Here are a few pictuers on my interests.

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    Last updated on June 5, 2003!

    get this gear!