A table of values of a function f with continuous gradient is given. Find of- dr, where C has the parametric equations below. * -.1 y-+: ostsi 1 18 2 257 6 2.

Q: 7 Determine the gradient function of y %3D ४

A: Given y = x^(7/3) Gradient of function is slope of function. Gradient = slope = dy/dx…

Q: Find the gradient of the function at the given point. Function Point f(x, у, 2) : x2 + y2 + z? (7,…

A: Formula for the directional derivative of the function f(x,y,z) is: ∇f = fxi +fyj +fzk Where…

Q: a) Find an equation of the tangent plane to the surface at the given point. xyz = 15, (1, 3, 5) b)…

A:

Q: Find the gradient of /x, y. 2) eand the largest value of the directional derivative of fox. y. zi…

A:

Q: 2. Find the equation of the tangent plane to the surface z = 3++ at point (-4, 3).

A: Topic- application of derivatives  Tangent to surface

Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,3) on the surface…

A: Given problem:- Find the equation for the tangent plane and the normal line at the point Po(1,1,3)…

Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,3) on the surface…

A: Given problem:- Find the equation for the tangent plane and the normal line at the point Po(1,1,3)…

Q: If the gradient of f is Vƒ = z j - yi – 2xzk and the poi f(x, y, z) = 0, find an equation for the…

A:

Q: Find the gradient of the function at the given point. Function Point f(x, у, 2) 3 x2 + y2 + z2 (7,…

A:

Q: Find the gradient of the function and the maximum value of the directional derivative at the…

A: Gradient of a function f(x,y,z) is given by,          grad(f(x,y,z))=i∂∂x+j∂∂y+k∂∂zf(x,y,z)…

Q: Find for the equations for tangent plane and normal line at P,on the given surface 2 х2 — Зху — у?…

A:

Q: The parametric equations of a curve are given by x = In (VE +1) and y = cosh-' (2t). dy when t = 1.…

A: Given x=lnt+1 and y=cosh−12t We have to find the dydx when t=1 We know that dydx=dydtdxdt.....1…

Q: The level curves of the surface z =x +y are circles in the xy-plane centered at the origin. Without…

A: Consider the given surface. z=x2+y2 The objective of the problem is to find the direction of the…

Q: Find the gradient of the function at the given point. y Ri (2, 2) x²+ y2' Vf(2, 2) = %3D Find the…

A:

Q: Determine the parametric equation for a line that is tangent (intersection) of the two fields below:…

A: We have to find out parametric equation for a line that is tangent (intersection)of the two fields…

Q: Find parametric equations of the normal line to the surface z = + y? at the point (2, -2,5) x = 2 -…

A: Let F(x,y,z) define a surface that is differentiable at (x0,y0,z0) then the normal line to F(x,y,z)…

Q: Find an equation of the tangent plane to the surface z = 16 − x2 − y2 at the given point (2, 2, 8)…

A: To Determine: Find an equation of the tangent plane to the surface z = 16 − x2 − y2 at the given…

Q: Find parametric equations for the line tangent to the curves of intersection of the surfaces xyz =1…

A:

Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx² + y2 + z2 (4,…

A:

Q: Find an equation for the tangent plane to z-x-y = 3 at the point (2, 1, 8) Z - ) %3D

A: given z-x2-y2=3 at point 2,1,8

Q: find the gradient of function f [x, y,z] = 3x² -y?_z? at paint {i,-Ź, -¡}

A: The given function is fx,y,z=3x2-y3-z2 and the given point is 1,-2,-1. The gradient of the function…

Q: A line passes through the point Po(xo, Yo) and has gradient m = tan a. Show that a general point of…

A: Gradient, or slope of a line characterizes the direction of the line and is found out by dividing…

Q: EXERCISE 2 Consider f(x, y) = 3x² – 4y² and U = %3D = cos î + sin r î. Use the Theorem above to find…

A: Here, the given function is: f(x,y)=3x2-4y2 which is differentiable. And, U→=cos 13π i^+sin 13π j^

Q: The parametric equations of a curve are given by x = In (VE +1) and Vt + y = cosh-(2t). X = dy when…

A:

Q: If the gradient of f is ∇f=yj⃗ −xi⃗ −4zyk⃗  and the point P=(−7,−8,−3) lies on the level surface…

A: an equation for the tangent plane to the surface at the point P

Q: Find an equation of the tangent plane to the given surface at the specified point. z3 бх2 + у2 - 7у,…

A: Solved below...

Q: Find an equation of the tangent plane to the surface y ln xz2 = 2, at the given point (e, 2, 1) and…

A: Given: ylnxz2=2 at the given point e,2,1

Q: If f(x, y) = xy, find the gradient vector Vf(7, 5) and use it to find the tangent line to the level…

A:

Q: Find the gradient of the function at the given point. w = x tan(y + z), (10, 5, -2) 2, Vw(10, 5, -2)…

A:

Q: A line passes through the point P0(x0, y0) and has gradient m = tan α. Show that a general point of…

A:

Q: 4. Find an equation of the tangent plane to the surface x = u? + 1, y = v + 1, z = u + v at the…

A:

Q: a) Compute the gradient of the function f(x, y, z) = e*y² . b)Compute the directional derivative Daf…

A:

Q: In what directjon from the point ( 1, 3, 2 ) is the directional derivative of 6 = 2 xz-y a maximum ?…

A:

Q: Find the gradient of the function at the given point. Function Point f(x, у) %3D х2 + 2ху (2, 4)…

A:

Q: Find the gradient of the function at the given point. Function g(x, y) = ye-* Vg(0,4)= Point (0,4)…

A:

Q: Find the gradient of the function and the maximum value of the directional derivate at the given…

A:

Q: 3/Find the equation for the tangent plane and normal line to the surface Z=9-x² + y² at the point…

A:

Q: Find an equation of the tangent plane to the surface at the given point. z = 8 – (3, –4, 4)

A:

Q: u =1-1,y=6-2+름 x = 1-, y = 6-

A: We have given parametric equations x=1-1t, y=6-7t+2t2. First, evaluate the first derivative dydx. To…

Q: Find an equation of the tangent plane to the surface at the given point. x² + y2 + z2 = 33, (1, 4,…

A:

Q: The level curves of the surface z = x2 + y2 are circles in the xy-plane centered at the origin.…

A: Consider , Equation of the surface given:  z = x2 + y2 The level plot is as shown below:

Q: Write parametric equations for the tangent line to the curve of intersection of the surfaces x =…

A: To find: The parametric equations for the tangent line to the curve of the intersection of the…

Q: (a) Find an equation of the tangent plane to the surface at the given point. z = x² - y², (5, 3, 16)…

A:

Q: 2. Find an equation of the tangent plane to the parametric surface F(u, v) = (, 2uv, uv?) at the…

A: (2) Consider the provided question,

Q: b) Find the equations of Tangent plane and Normal line of the surface: z3 + xyz – 2=0 at Po(1,1,1)

A:

Q: Find an equation of the tangent plane to the surface z = √(9 − x2 − y2), at the given point (1, 2,…

A: The surface given is Fx,y,z=√(9 -x2 -y2) -z =0. The derivative of the surface coordinates with…

Q: find equations for the(a) tangent plane and(b) normal line at the point P0 on the given surface. x2…

A: Consider the function fx,y,z=x2+y2-z2-18. ∇fx,y,z=fx, fy, fz=2x, 2y, -2z. At 3, 5, -4, ∇f3, 5,…

Q: Vhat is the gradient of g(x.y) = ye* and its maximum value of its directional derivative at P(0, 5)?…

A:

Q: Find an equation of the tangent plane to the surface at the given point. - . z = 8 —х — у, 3 (3, –4,…

A: Given plane is z=8−83x−y. We have to find the equation of tangent plane to the surface at the point…