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3. Find aw for w2 + w sin(xyz) - 0. ax ox Fx 4. Find two unit vectors orthogonal to both u = 1+2 and v = 3i - k. 5. Find the directional derivative of S(x, y) - 3zły at the point (1.2) in the direction of v = 31 +4J. 6. For the function f(x, y, z) = e, find the maximum value of the directional derivative at the point (1.2.3). VELIVE ... 7. Evaluate the integral: (sin ti + 1*] + k)dt. 8. Find r(t) given that a(t) = 1 + ej, ro) - 2) and r(0) - 21. 9. Let r(t) = 4 cos ti + 4 sin tj + 2tk. Find the unit tangent vector 10. Find the length of the space curve represented by the vector valued function r() - 11+] + 1/2, 2 s 157. 11. Find the first partial derivative with respect to y: F(x, y, ) - arctan dw 12. Use the appropriate Chain Rule to find when t = -1 forw = -: -- 1 - A dr y=2+3. z = 2 + Houghton Mifflin Company. All rights reserved. 13. Find the domain of the vector-valued function r(t) - 2/1 + r) + Intk. (sin( - )) + + COSTIK Find the limit: lim K] 14. 1-1 15. Let r(t) = r sin ti + costj+rk. Find (m). 16. Calculate the speed of the object having the position vector r(t) = sin ti + cos tj - 16k at the point where - 1.