Each Problem is worth 5 points. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Problems 1-5: Find the gradient field F of the function f. 1) f(x, y. z) - xby5 + x3 z2 1) A) F - (6x5 + 5x4)i + 5y4j + 2k B) F - (6x5 + 5x4)i + 5y4j - 2k C) F - 6x5y5 + 5x4 1 + 5xby4; _ 2x5 23 - k D) F - 6x5y5i + 5xby4; _ 2x6 23 2) f(x, y. z) = x33x + y4z3 2) A) F - (1 + x)x23xi + y323j+ y4z2k B) F - (3 + 3x)x23Xi + (x33x + 4y323)j + (x33x + 34z2)k C) F - (3 + 3x)x23xi + 4y323j + 3y4z2k D) F - (3 + 3x)x23xi + 4y3j + 3z2k3) f(x, y, z) _ x2 + y2 + z2 x 6 3) A) F -4x2 - by2 - 672. -i+ 2; $ 22k B) F 8x2 + by2 + 672 . 2y; 22 x6 x7 x6 x6 C) Fi + 2yj + 2zk * 7 D) F - (x2 + y2 + z2)i + 2y; 4 2zk * 6 4) f(x, y. z) mex 10 + y" + 24 4) A) F = 10x9ex10 + y9 + 24; + gyBex10 + y9 + 24; + 4232x10 + y9 + 24k B) F = 10x9ex 101 + gyBey"; + 423e Z4 k C) F = x9ex10 + y9 + zi + yBe*10 + y9 + 24; + 23ex10 + y9 + 24k D) F = x 10ex 10 + y9 + 24; + y9ex10 + y9 + 24; + 24ex10 +y9 + 24k 5) f(x, y, z) = z sin (x + y + z) 5) A) F - z cos(x + y + z)i + z cos(x + y +z)j + (sin(x + y + z) + zcos(x + y + z))k B) F - cos xi + cos yj + (sin z + z cos z)k C) F = -z cos(x + y + z)i - z cos(x + y +z)j + (sin(x + y + z) - zcos(x + y + z))k D) F - -cos xi - cos yj + (sin z - z cos z)k