** Please answer two parts of the questions.
Part 2 out of 2:
f y (1,0) = _________________
** Please answer two parts of the questions. Part 2 out of 2: f y (1,0)...
Let H=F(x,y) and x=g(s,t), y=k(s,t) be differentiable functions. Now suppose that g(1,0)=8, k(1,0)=4, gs(1,0)=8, gt(1,0)=2, ks(1,0)=1, kt(1,0)=5, F(1,0)=9, F(8,4)=3, Fx(1,0)=13, Fy(1,0)=7, Fx(8,4)=9, Fy(8,4)=2. Find Hs(1,0), that is, the partial derivative of H with respect to s, evaluated at s=1 and t=0.
For questions 3-8: 5y2 Let f(x, y) = + y 2 Find the two first partial derivatives and the four second partial derivatives of f at the point (1, -2). Question 6 Find fry (1,-2). Question 7 Find fy (1, -2). D Question 8 Find fy: (1, -2).
Question 8 Let f(x, y) = ln(x + 2y). What is the maximum rate of change of fat P(1,0)? Formulas: The maximum rate of change of f at P(20, yo) is | Vf(x0,yo) = V(fx (30, yo))2 + (fy(20, yo))? The gradient of fis f(x,y) = (fa(z,y), fy (z,y)) and substitute * = 0, y = yo into V f(a,y) to get f(go,yo) of f at the point P(0.yo)
Can you evaluate without Green's Theorem? If so, please show your work. Suppose that f(x, y) has continuous second-order partial derivatives, and let C be the unit circle oriented counterclockwise. What is / [fx(x, y) – 2y] dx + [fy(x, y) + x] dy?
please all questions (only answer ) (1 point) In 1932, Giuseppe Momo was commissioned to build the famous Vatican Museum double spiral staircase. Suppose that it takes you one hour to stroll at a constant speed up one spiral of this staircase, which has a radius of 25 feet and a height of 54 feet and makes 6 revolutions. (a) Assuming the spiral staircase is centered about the z-axis, find a vector parametric equation for the helical path you take...
8.) (10 Points) Given the contour diagram z = f(x,y). 2 1 2 3 4 -2 R a. Find i. f(-1,1) 11. a value of x for which f(x, 1) = 3 iii. a value of y for which f(0,y) = -2 b. The given graph has a local maximum value. At which point (x,y) does this occur? c. Determine the sign (positive or negative) of the following partial derivatives. i. (1,0) ii. fy(0,1)
1.Find the partial derivatives of the function f(x,y)=(8x+8y)/(6x-7y) fx(x,y)= fy(x,y)=
Problem 5. (1 point) Find all the first and second order partial derivatives of f(x,y) 7 sin(2x + y) + 9 cos(x - y). A. = fx(x,y) = B. = fy(x, y) = af C. ar2 = fcz(x, y) = af D. ay2 = fyy(x,y) = E. af деду fyz(x, y) = af F. მყმz = fxy(x, y) = Note: You can earn partial credit on this problem.
the function of two real variables defined below: 1 –9x + 2y“ (x, y) + (0,0), f(x, y) = { 6x + 3y 10 (x, y) = (0,0). Use the limit definition of partial derivatives to compute the following partial derivatives. Enter "DNE" if the derivative does not exist. fx(0,0) = DNE fy(0,0) = 0
Problem #8: Let f(x, y, z) = xzly. Find the value of the following partial derivatives. (a) fx(4,3,2) (b) fy(4,4,4) (c) fz(3,4,3)