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trace the conic x2+2xy+y2-3x+y-2=-0
Find dy/dx and d²y/dx² without eliminating the parameter.
a.) x= e^(2t) , y= t In(t)
b.) x= sinh(t) , y= cosh(t)
c.) x= 1-t^2 , y= 1+t
Find dy/dx and d^2y/dx^2 without eliminating the parameter.
1. x=1-t^2 ; y=1+t
Find the mass of the solid in the shape of the tetrahedron that is bounded by the planes x + y + z = 1 , xy- plane, xz- plane and yz- plane if its density is given by 𝛿(x, y, z) = x
Limit x approach infinity x[ ( 1 + a/x )^1+1/x - x^-1/x ( x+ a ) ]
Find all intervals on which the function f(x)=(-x+2)e^-x is increasing. If there is no such interval, submit an empty answer.
A police car is located 70 feet to the side of a straight road.
A red car is driving along the road in the direction of the police car and is 100 feet up the road from the location of the police car. The police radar reads that the distance between the police car and the red car is decreasing at a rate of 70 feet per second. How fast is the red car actually traveling along the road?
A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.3 cm/min. At what rate is the volume of the snowball decreasing when the radius is 9 cm. (Note the answer is a positive number).
Considering the volume of a spherical shell as an increment of volume of sphere, find approximately the volume of a spherical shell whose outer diameter is 8 inches and whose thickness is 1/16 inch.
