Compute the line integral of the scalar function f(x, y) = /1+ 9ry over the curve y = x° for 0 <¤ < 1 Se F(x, y) ds =
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- Let u(t) = 21'i+ (-1)j-8k. Compute the derivative of the following function. (11 +7t) u(t) Select the corect choice below and fill in the answer box(es) to complete your choice. O A. The derivative is the scalar function O B. The derivative is the vector-valued function Di+ i+ k. Click to select and enter your answer(s) and then click Check Answerlinearise R = AT + BT2Consider the function defined by f(x,y) = 4xy - 2x2. Evaluate the directional derivative of f at point(1,-1) in direction of the vector which subtends an angle of pi/6 with the positive x-axis.
- State what it means for a scalar function y = f (x) to beintegrable on an interval [a, b].Evaluate along the curve y=x2 from (-1,1) to (2,4). First find the vector valued function r(t) defining the curve.Ex.: Find the directional derivative of the function f(x, y) = x'y* + x*y* at the point (1,1) in the direction of the vector (4,3).
- Find the directional derivative of the function: f(x, y) z² + 4y at the point (0, 0) in the direction of the vector (– 3, 1). You may enter your answer as an expression or as a decimal with at least 4 significant figures. |Find both the parametric and vector equation of the line segment between (−2, 3) and (5, −1) where 0 ≤ t ≤ 1. Please show all your work.Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y) =8xy2, (5,-7) maximum rate of change direction vector