Calculus Answers

Find the function f whose tangent has slope (x^3-2/x^2+2) for each value of x and whose graph passes through the point ( 1, 3 ).

Determine whether the following series converge:
∑_(k=1)^∞〖(-1)〗^(k+1) (k+3)/(k(k+1))

Use a double integral to find the area enclosed by one loop of the four-leaved rose r =cos(2 theta).

Evaluate \int (1 to 4) dx/((x-2)^(2/3))

For what values of p does the integral \int ( 1 to +infinite) dx/(x^p) converge?

A fluid motion is given by V =(y +z) i + (z + x) j +(x+ y) k. Show that themotion is irrotational and hence find the velocity potential also show that motion inpossible for an incompressible fluid.

the height of an object falling from a cliff is given by h(t)= 520 - 30t -16t^2. the time measurement is correct to within 0.25 seconds. estimate the propagated error in computing the height of the object at time t=3 sec.

The area is bounded by the curve y=x^2+2 and the line y=x+8 is rotated around the x axis. Find the volume of the solid generated.