Given T(x, y, z) = x + z z-y a. Find the vector in the direction in which T(x, y, z) increases most rapidly at P(-3, −5, 2). Write the vector in component form and give all components in exact form. b. Find the maximum rate of increase of T(x, y, z) at P(−3, –5, 2). c. Find the rate of change of T(x, y, z) at P(−3, −5, 2) in the direction of Q(-1, -7,1).

Q: Find the maximum rate of change of f(x, y) = ln(x² + y2) at the point (-3, -5) and the direction in…

A:

Q: Let f(x, y) = x6y4. Round the components of your answers to three decimal places. (a) At the point…

A: Please see the below picture for detailed solution.

Q: 2yy" = 1 + (y')² 2

A:

Q: f(x, y, z)=1/√√√x² + y² + z² P(-1,2,2) = -3i+27-3k

A:

Q: Repeat Exercise 27 for the forces KX = (2, – 3) and KY = (- 2, 3).

A: The given two force vectors are, KX→=2,-3KY→=-2,3 When we find the addition of two vectors, then the…

Q: Calculate the directional derivative of f(x, y) = x²y in the direction of v = −3i+2j at the point P…

A:

Q: Given f(x, y, z) = 3x² + xy-2y²-yz + 2², find the rate of change of f(x, y, z) at (1, -2, -1) in the…

A:

Q: Find the velocity vector v(t) and the acceleration vector a(t) of the straight line motion given by…

A: Consider the given question,The velocity vector v(t) from the given position vector is find as,

Q: Experiments show is that in temprature field, heat flows in the direction of maximum decrease of…

A: NOTE: According to guideline answer of first three subpart can be given, for other please ask in a…