参数曲线的微积分

Slope from the parameter

Higher derivatives and tangent lines

Arc length along a parametric curve

Surfaces of revolution

For x(t) = t squared and y(t) = 2t, what is the slope dy/dx at the parameter value t = 2?

For a parametric curve, at which parameter values does the curve have a vertical tangent line?

Which integrand gives the arc length of a parametric curve over the interval from a to b?

For x = 3t and y = 4t on the interval from 0 to 2, what is the arc length?

Which expression gives the area of the surface formed by revolving a parametric curve about the x axis?

For a curve given parametrically, which computation finds the tangent line's slope at a point?

For x(t) = t squared and y(t) = 2t, what is the slope dy/dx at t = 2? Give a decimal number.

For x(t) = t squared and y(t) = t cubed, what is the second derivative of y with respect to x at t = 1? Give a decimal number.

For x = 3t and y = 4t on the interval from 0 to 2, what is the arc length? Give a number.

For x(t) = t and y(t) = t squared, what is the slope dy/dx at t = 3? Give a number.