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AP Calculus Review - Parametric & Polar Functions

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Section 1

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Area Inside a Polar Curve

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Calculus Math

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Date created

Mar 1, 2020

Cards (22)

Section 1

(22 cards)

Area Inside a Polar Curve

Front

Back

Length of a Polar Curve

Front

Back

Cardioids

Front

Note the symmetry with respect to which axis

Back

For an object in motion along the curve P(t) = (x(t), y(t)), the velocity vector for v(t) is

Front

Back

For an object in motion along the curve P(t) = (x(t), y(t)), the speed is

Front

Back

The graph of r = aθ

Front

Spiral

Back

The graph of rθ = a

Front

Logarithmic Spiral

Back

To find r when converting rectangular coordinates (x, y) to polar form...

Front

x² + y² = r²

Back

If P(t) = (x(t), y(t)), then dy/dx =

Front

Back

If P(t) = (x(t), y(t)), then then dP(t) =

Front

(x'(t), y'(t))

Back

For an object in motion along the curve P(t) = (x(t), y(t)), the distance traveled is

Front

Back

Expressed in polar coordinates: y =

Front

y = r sinθ

Back

To find θ when converting rectangular coordinates (x, y) to polar form...

Front

tan θ = y/x

Back

If P(t) = (x(t), y(t)), then d²y/dx² =

Front

Back

Limaçons

Front

sin = symmetric across y-axis cos = symmetric across x-axis a>b then no loop a<b then loop

Back

Slope of a Polar Curve

Front

Back

For the curve where P(t) = (x(t), y(t)), the length of an arc =

Front

Back

Lemniscates

Front

Back

Expressed in polar coordinates: x =

Front

x = r cosθ

Back

The graph of r = k

Front

Circle

Back

For an object in motion along the curve P(t) = (x(t), y(t)), the acceleration vector for a(t) is

Front

Back

Roses

Front

Back