f(x, y) = e ^(x)/ x^2 cos y .

Find its gradient at an arbitrary point (x, y)

In which direction does the function change most rapidly at the point (0, )?

Find the directional derivative at the point (0, ) in the direction of the vector (1,1).

A wire has the shape described by the vector function

r(t) = sin ti + costj + t k , 0 t 2 .

The linear density varies along the wire according to the equation

(x, y, z) = x + y ^2 + z .

Find the total mass of the wire by evaluating the line integral

Z ds .

Leave your answer in exact form, that is do not replace numbers such as 2 or by decimal approximations (use the symbol in your answer).