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Questions by Sun from Los Angeles, CA

Find the curvature at the point (x, y) on the ellipse x^2/9+y^2/4=1.   x^2/a^2+y^2/b^2=1 x(t)=acos(t) y(t)=bsin(t) x(t)=3cos(t) y(t)=2sin(t) ---------------------------- k=abs(x'y"-y'x")/[(x')^2+(y')^2]^(3/2) k=6/(9sin^2...

A stone weighing 1/2 lb is thrown upward from an initial height of 5 ft with an initial speed of 32 ft/s. Air resistance is proportional to speed, with k=1/128 lb-s/ft. Find the maximum height attained...

A constant horizontal force of 10N pushes a 20kg-mass through a medium that resists its motion with 0.5N for every m/s of speed. The initial velocity of the mass is 7 m/s in the direction opposite...

Find the limit of y(t) as t approaches infinity for the initial value problem   y'=sin(y(t)), y(0)=pi/2.   The answer is pi. Please show all your work step by step. Thanks...