56. Let E(x, y, z) = tan-'(xy + 2z) + zex²-y² + z and let r(t) = (h(t), et²-2t, t²-3t+3) be a parametrization of a curve in space where h(t) is a differentiable function where h(2) = -1 and h'(2) = 4. (a) Find the value of the constant a such that the rate of change of E at the point (x, y, z) = (2,2, -1) in the direction of (x,-1,2) is 18/5. (b) Let ß represent the rate of change of E with respect to t along the path r(t) at t = 2. Find the value of the constant B.

Q: Let h be a differentiable function of z obtained from the parametric equations z = f(t), y = 9(t).…

A: Option  1  is true .

Q: given f(z)=u(x,y)+iv(x,y) is an analytic function where u(x,y)=x^3-3xy^2. find f(z)

A: We have to find .

Q: Find a function y = f(x) that describes the parametric x = -2t + 1, y = 3t², for – o <t < ∞. curve

A:

Q: Sketch the slope field for y’ + y = 2 at the 25 gridpoints (x, y), where x = 0, 1, ... ,4 and y = 0,…

A: The given differential equation is y'+y=2. Sketch the slope field for the above equation as shown…

Q: 20-21) What is the equation of the tangent line to y = x3 at x=2? A) y = x - 12 B) y = 12x C) y = x-…

A: Use derivative for finding the  equation of tangent line .

Q: Let g(u) be a differentiable function, and let f(x, y) = g(x^2,y^2)   Find the direction of…

A: Given that gu be the differential function and let fx,y=gx2,y2 We have to find the direction of…

Q: 6) What is the tangent plane of f (x, y) = 5x² – 2xy? + 3xy + 4x at point (xo, Yo) = (1, –2) ?

A: The question is solved in step. 2

Q: For the function f(x,y) = 100 - x^2 - y^2 a) Draw the cross-section of f(x,y) with x fixed at x =…

A: "Since you have posted a question with multisubparts, we will solve the first three subparts for…

Q: Let h be a differentiable function of x obtained from the parametric equations a = f(t), y= g(t) .…

A: if x=f(t) and y=g(t) thendydx=dydtdxdt

Q: 6. Show that (an)neN C R is bounded if and only if lim supn→∞ an < +∞o.

A: To Prove:  ann is bounded sequence if and only if limsupan&lt;+∞.

Q: Find domain and vange f (2y)- し、 (x'+ゴ) ) fCz, y) = Sin" (y-z) Ž (3,y)- tan

A: According to the question,  We need to specify the domain and range of the given function: (A) f(x,…

Q: 11- Find the moment of inertia about x-axis bounded by the curve y = 6- x² and the line y = x + 1

A: The given information in the question is the curve y=6-x2 and the line y = x + 1. The objective is…

Q: Let be a curve in the xy-plane. Find d'y dx² -|(x, y)=(1, 1) = _ 6x³3 + 19y³ = 25 તે પુ da²(x,…

A:

Q: Evaluate d:/dx on the surface x: + + x²y®=² = 3 at the point (1, 1, 1).

A:

Q: Sketch the curve r(t)=f°i+tj and indicate the orientation. Find r'(t) and sketch r(1) & r°(1).

A: First we will plot the given parameters.

Q: iv is analytic = -11..

A:

Q: Q4) Consider the function f(x,y,z) = x³ – xy² – zy a) Find the derivative of f(x, y, z) in the…

A: Given function fx,y,z=x3-xy2-zy a) Directional derivative, D=∇f·A⏜…

Q: 1.Solve the following polynomial equations.  a)  2X3+1=x2+2X

A: