Find the curvature, the radius of curvature and the center of curvature having a parametric equations at the given point:
x = sin y, (1/2,1/6 π)
Find the slope of the curve and the equation of tangent line of the parametric equation to the given point.
x=ln t , y = t ^ - 1 , when t = 2
Find the slope of the curve and the equation of tangent line of the parametric equation to the given point.
5. x=√t , y = 2t + 4 , t=1
Find the first and second derivatives of the following and simplify whenever possible:
x = a cosh t; y=b sinh t
Find the first and second derivatives of the following and simplify whenever possible:
x = t ^ 2 * e ^ t y = t In t
Find the first and second derivatives of the following and simplify whenever possible:
x=e^t: y=te^-t
Find the first and second derivatives of the following and simplify whenever possible:
x = 9t ^ 2 - 1 : y = 3t+1
Find the limit of 2x(x-2)/x-2 as x is 2
x^ 2 y^ " - 2xy'-4y=x^ 2 +2 log x
Determine the critical numbers of the given function and classify each critical point
as a relative maximum, a relative minimum, or neither.
ff(tt) = tt2
tt2 + tt − 2 .