<Text-field style="Heading 1" layout="Heading 1">Problem 0 (attendance

<Text-field style="Heading 1" layout="Heading 1">Problem 1 (Pi - 4 points)</Text-field>

The formula for the area of a circle of radius r is equal to 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This formula can be derived using integration to compute the area under the curve defined by a circle of radius r in the first quadrant and then multiplying by 4.

with(plots): with(plottools):

Warning, the name changecoords has been redefined

Warning, the assigned name arrow now has a global binding

c := circle([0,0],1): l := line([0,0],[cos(Pi/6),sin(Pi/6)]): p := point([cos(Pi/6),sin(Pi/6)]): lp := line([cos(Pi/6),0],[cos(Pi/6),sin(Pi/6)]):

display({c,l,lp,p});

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

Let the point indicated in the above figure have coordinates [x,y], and using the fact that 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 down a definite integral for the area of the circle in the first quadrant. Use Maple to verify that 4 times this integral is equal to 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

A numerical approximation to pi can be obtained by approximating the area under the curve as was done in lab 2. The following two function

# Approximate the area under the curve defined by f on the interval [a,b] using N rectangles. # Inputs: f : a Maple function of a single variable, which must be continuous. # a, b : real numbers such that a < b. N : a positive integer. # Output: an approximation to Int(f(x),x=a..b) obtained by the sum of N equally spaced rectangles. Approx := proc(f,a,b,N)

local h;

h := (b-a)/N;

return add(f(a+i*h)*h,i=1..N);

end;

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

# plot a function and boxes approximating the area under the curve defined by the function on an interval. # Inputs: f : a Maple function of a single variable, which must be continuous. # a, b : real numbers such that a < b. N : a positive integer. # Output: a plot structure showing f on the interval [a,b] and N equally spaced boxes whose heights are # defined by value of f on the left endpoint of the subinterval defining the base of the box. plotboxes := proc(f,a,b,N)

local polys, i, h, x, C; h := (b-a)/N;

polys := seq(plottools[rectangle]([a+(i-1)*h,0],[a+i*h,f(a+i*h)],transparency=1),i=1..N);

C := plot(f(x),x=a..b);

return `PLOT`(polys,op(C));

end;

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

Define a maple function, using the arrow notation, for the curve defined by the circle 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The function should define 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as a function of 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

Use plotboxes to show how the area of the circle in the first quadrant would be approximated with 10 boxes. Then use Approx to estimate 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using different values of 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