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Curve

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AP Calculus AB/BC

Definition

A line that is not straight and may have varying slopes or shapes.

"Curve" also found in:

Subjects (4)

Practice Questions (8)

What is the volume of the solid obtained by rotating the region bounded by the curve y = √x, the line y = 1, and the lines x = 1 and x = 4 around the line y = 1?
What is the volume of the solid formed by rotating the region bounded by the curve y = 1/x, the line y = 0, and the lines x = 1 and x = 2 around the y-axis?
The arc length of a curve is always _______ the displacement of an object along the curve.
Henry draws a heart defined by the parametric equations x(t) = sin(t) and y(t) = 1 + cos(t) - cos^2(t). What is the slope dy/dx of the curve at the point (sqrt(3)/2, 5/4)?
Henry draws a heart defined by the parametric equations x(t) = sin(t) and y(t) = 1 + cos(t) - cos^2(t). What is the concavity of the curve at the point (sqrt(3)/2, 5/4)?
Consider the parametric equations: x(t) = t^2 y(t) = 3t What is the arc length of the curve between t = 0 and t = 2?
Consider the parametric equations: x(t) = t^2 - 1 y(t) = t^3 + 2t What is the arc length of the curve between t = -1 and t = 1?
A particle moves along a curve in the plane with a velocity vector given by v(t) = ⟨2t, 4t^3⟩. If the particle’s initial position is ⟨1, 4⟩, what is the position vector of the particle at time t = 2?

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