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- What does it mean for the differentiability of a function if only one of the Cauchy-Reimann equations (Ux = Vy and Vx = -Uy) holds?Suppose z is given implicitly by the equation x3y-yz2+z/x=4 in a neighborhood of the point P (1, −2), in which z = −2. The value of the directional derivative of z at P in the direction of the vector w = (−3, −4), corresponds to:Suppose z is given implicitly by the equation ln (yz2) + x3z = −1 in a neighborhood of the point P (1, 1), in which z = −1. The value of the directional derivative of z at P in the direction of the vector w = (−1, 1), corresponds to: the answers are in the first attached image
- Suppose z is given implicitly by the equation ln (yz2) + x3z = 1 in a neighborhood of the point P (1, 1), in which z = 1. The value of the directional derivative of z at P in the direction of the vector w = (1, −1), corresponds to:Find a vector equation for the tangent line to the curve of intersection of the cylinders x2+y2=25 and y2+z2=20 at the point (3, 4, 2).give the position vectors of particles moving alongvarious curves in the xy-plane. In each case, find the particle’s velocityand acceleration vectors at the stated times, and sketch them asvectors on the curve. Motion on the parabola y = x2 + 1r(t) = ti + (t2 + 1)j; t = -1, 0, and 1
- What does it mean for the differentiability of a function if the Cauchy-Reimann equations (Ux = Vy and Vx = -Uy) do not hold?If an object travels in the xy-plane along the curve traced out by the vector function r(t) = (t 3/2,-t) for t ≥ 0, then the total distance traveled by the object from t = 0 to t = 4 isSketch the slope field and solution curves a) yy' + 4x = 0, (1,1), (0,2) b) y' = 1-y^2, (0,0), (2, 1/2)