Consider the vector field F ty2 -i+÷j+x²zk over the surface S where S is the sphere x2 + уз y2 + z? = 4, with outward orientation. (a) Examine the vector field F and the surface S. Without computation, determine if the flux of F across S is positive or negative. Explain. (b) Compute div F. Does your answer support your claim in part (a)? How? (c) Use the Divergence Theorem to find the flux of F across S.

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