Equation for tangent line in cartesian coordinates

Find equation of tangent line in cartesian coordinates. Give in polar coordinates: r=3-2costheta, at theta=pie divided by 3.

Length of curve

length of curve interval [0,4] y= x (to the three halves) minus 1 y=x^3/2 - 1

Arc length

The definite integral for arc length is given in any first year calculus book. The equation for a projectile is in the form of a parabola and can be found in any first year physics book. What I need is an equation for the arc length in terms of the initial angle of launch and the horizontal distance traveled (X).

Arc length of graph of function for a given interval.

What is the arc length of the graph of function y=x (to the 2/3)-1 interval[0,4] ?

Volume Calculation of a Cone: Changing radius at Constant Height

Derive a formula that estimates the change that occurs in the volume of a right circular cone when the radius changes from r0 to r1 and the height does not change.

Volume of Revolution: Parabola and Lines

Find the volume of the solid generated by revolving the region between the parabola x = y^2 + 1 and the line x =3 about the line x =3.

Differentiation: Word problem - rate of change

A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1m higher than the bow of the boat. If the rope is pulled in at a rate of 1m/s, how fast is the boat approaching the dock when it is 8m from the dock?

Differentiation: Word problem - rate of change

A water trough is 10 m long and a cross-section has the shape of an isosceles trapezoid that is 30cm wide at the bottom, 80 cm wide at the top, and has a height of 50 cm. If the trough is being filled with water at a rate of 0.2m3/min, how fast is the water level rising when the water is 30cm deep?

Minimization

A box with a square base and open top must have a volume of 32,000cm3. Find the dimensions of the box that minimize the amount of amount of material used.

Functions: Limits

Lim [1/(x-1) - 2/(x-1)] x→1