Calculus Answers

By using divergence theory compute the surface integral of ∫ ∫T F.ds where T is the unit spehere x^2+y^2+Z^2=1. and the vector field F is (y,z,x).

I found the div(F)=0 so the surface integral is zero? Is this correct? Could someone please confirm? Thank you!

Find the volume of the solid obtained by
rotating the region bounded by x = 4y^2 - y^3 , x = 0 about y = 0

integrate 1/w(4-2w)^1/2

A rich uncle wants to make you a millionaire. How much money must he deposit in a trust fund paying 7% compounded continuously at the time of your birth to yield $1,000,000 when you retire at age 62?

$1,000,000=Pe^(.07x62)

Not sure how to eliminate the Pe in order to bring down the (.07x62) and eventually divide 1,000,000 by it.

A rich uncle wants to make you a millionaire. How much money must he deposit in a trust fund paying 7% compounded quarterly at the time of your birth to yield $1,000,000 when you retire at age 56? (Round your answer to the nearest cent.)

. Determine whether 1+1/2-1/3-1/4+1/5+1/6-1/7-1/8+1/9+...converges or diverges

Consider two ships which are joined by a cable attached to each ship at the water line. Suppose the two ships are 200 metres apart, with the cable stretched tight and attached to a pulley which is anchored halfway between the ships at a depth of 45 metres. If one ship moves away from the other at 3 km/h,how quickly is the other ship moving after one minute?