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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 .


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