(a) Find an equation of the plane tangent to the surface f(x, y) = xy² – 5x at the point (1, 2, – 1). | (b) Find the linearization L(x, y) of the function in part (a) near the given point. Use this function to approximate the value of f(0.99, 2.02) by hand.

Q: 4. For the function f(x,y) = 2x² – 3xy + 8y? + 2x – 4y + 4, find a tangent vector to the level curve…

A:

Q: 03. The equation of the tangent plane to the surface f(x,y) at the point (1,1) is 2x + 2y = 9, find:…

A: We have given equation of tangent plane 2x+2y=9which is incorrect because left side is even number…

Q: An equation of the tangent plane to the surface 1+y z = at the point p(1, 3, 2) is 1+x (A) (x-1) -…

A:

Q: 1. Find the equation of the tangent plane to the given surface at the specified point. (a) f(x, y) =…

A:

Q: (a) Find an equation of the tangent plane to the surface at the given point. x² + y2 + z2 = 26, (1,…

A: Given problem:- (a) Find an equation of the tangent plane to the surface at the given point.   x2 +…

Q: If the gradient of f is ∇f=y3j−xi+zyk and the point P=(−8,6,2) lies on the level surface f(x,y,z)=0,…

A: To find the equation

Q: Find an equation for the tangent plane to cos(rx) – x²y+ e*z + yz = -4 at the point (0, 1, –6). = 0.…

A:

Q: An equation of the tangent plane to the surface 1+y Z = at the point p(1, 7, 4) is 1+x (A) 2(x+1) -…

A:

Q: 03. The equation of the tangent plane to the surface f(x, y) at the point (1,1) is 2x + 2y = 9,…

A: the surface is fx,y the gradient to the surface at (1,1) is ∇fx,y Let the value of the gradient is…

Q: Q9. Find the equation of the tangent plane to f(x, y) = x ln(y) +x²y+3 at the point (x, y) = (2, 1).…

A:

Q: 1. Let f(x, y) = -x2 – xy³ + 7. Find an equation for the plane tangent to f at (3, 2).

A:

Q: Find the equation of the tangent plane to z=e^y+x+x^2+10 at the point (2,0,17).

A:

Q: Find the equation of the plane tangent to the surface f(x,y) = x In(x y) at the point (1, e).

A: We will find the equation of tangent plane to the given surface.

Q: (a) Find an equation of the tangent plane to the surface at the given point. xyz = 20, (1, 4, 5) (b)…

A:

Q: The tangent line to the curve r(t) =(t°,t“, t³ ) at the point (1, 1, 1) intersects the æy-plane at a…

A:

Q: dz (a) Use an appropriate form of the chain rule to find dx dz in terms of y in terms of x and if z…

A:

Q: Find the moment of inertia with respect to the y-axis of the curve x2 = 8y bounded by the line y = 2…

A:

Q: Let f(x, y) = 2xy – 4x² + 3y². %3D Then a standard equation for the tangent plane to the graph of f…

A: The function is given. Find the partial derivative fx and fy at the given point. Given,…

Q: 3. Find the parametric equation for the line tangent to the curve of intersection of the surfaces x²…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 4) Find the equation of the tangent plane to the surface r(u, v) = (u²-v²)i − (3uv)j + (4√u+v)k when…

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: Let f(x, y) = x³ √√y. A. Find an equation for the plane tangent to the graph z = (x, y) = (1,4). B.…

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: (a) Find an equation of the tangent plane to the surface at the given point. xyz = 8, (1, 2, 4) (b)…

A:

Q: Find the gradient of the ellipse 2x2 + 3y2 = 14 at the points where x = 1

A: Consider the given equation of the ellipse, 2x2+3y2=14 here we need to find the gradient of the…

Q: 7. Find the equation of the tangent plane to each surface at the given point. (a) x? + y? + z² = 14…

A:

Q: Find the linearization L(x,y) of the function f(x,y) = e (X cos (5y) at the points (0,0) and 0,- 2

A:

Q: Find the extremum and saddle points of the function f(x, y) = x3 – 3xy + y3 if any. Compute cch of…

A: As per our guidelines,only one question can be solved, Solution for B is given below:

Q: 48. Let f(x, y, z) = xyz + 3. Find an equation of the level surface that passes through the point…

A: Given that: f(x, y, z)=xyz+3

Q: Find equations for (a) the tangent plane and (b) normal line at the point P on the given surface 1)…

A:

Q: Q3: For the surface f (x, y, z) = In (xyz), find: (1) the gradient of f at (1,1,2), (2) the…

A: Given

Q: If the gradient of f is Vf = r'j- 3yi+ 2zz k and the point P = (-4,-4, 1) lies on the level surface…

A:

Q: Let f(æ, y) = x² + 4y² – 5. (1) Find the equation of the plane tangent to this function at (1, 1,…

A: Given f(x,y)=x2+4y2-5. We find the equation of the plane tangent to this function f(x,y) at (1,1,0).

Q: ) Find the linearization L(x, y) of the function f(x, y) = ez+y at (0,0). Use it to estimate f(0.01,…

A:

Q: 2. Find an equation for the plane tangent to the surface 3x2 - 4xy+ z2 = 0 at the point (1, 1, 1).…

A:

Q: Let f (x,y)=x2+5xy−4y2. Then a standard equation for the tangent plane to the graph of f at the…

A:

Q: Q5: Find equations for (a) the tangent plane and (b) normal line at the point P, on the given…

A: Given that  The equation  cos(πx)-x^2y+e^(xx)+yz=4  Point (0,1,2) To find the equation of the…

Q: 4. Let g(x, y) = e"/v, Find an equation for the tangent plane at (x, y) = (2, 1).

A:

Q: Q5: Find equations for (a) the tangent plane and (b) normal line at the point P, on the given…

A:

Q: Please help solve this. If this can be solved without linear algebra I would prefer to see that…

A:

Q: Let f(x, y) = 4x²y² – 2x² a) Find fx(2, 1) b) Find fy(2, 1) c) Write the equation for the tangent…

A: given function:-   f(x , y) = 4x2y2 - 2x2

Q: ) Compute the directional derivative of f(x, y) = x2 y at the point (1, 1) in a direction normal to…

A:

Q: If the gradient of f is Vf = x³ } – zỉ+ 2yx k and the point P = ( surface f (x, y, z) = 0, find an…

A:

Q: Find the equation of the plane tangent to the surface f(x, y) = x In(x y) at the point (1, e).

A:

Q: (a) Find a function f(x, y) with gradient F, where F = (y cos(xy), x cos(ry) + y² +2y) (b) Use your…

A: (a)According to question given :F→=y cos(xy), x cos(xy)+y2+2yWe have to calculate for f(x,y)As we…

Q: Show that the curve r(t) = ( t3 /4 - 2)i +(4/t-3)j+cos(t-2)k is tangent to the surface x3 + y3 + z3…

A:

Q: Find the linearization of the function f (x, y, z) = -6xy+ 9yz + 8zx at the point (1, 1, 1)

A:

Q: (a) Find the equation of the tangent plane to the surface z = f(x, y) = /T= a² – y² at the point…

A:

Q: Example 1. Let f(x, y) = (y + 1)e²+v°, (a) Find the tangent plane to f at the point (0,0).

A:

Q: Find the linearization of the function f(x, y, z) = xy+ yz + zx at the point (1,1,1).

A: Linearization of the function f(x,y,z) at (a, b, c) is given by…

Q: 1. Determine the directional derivative of the surface f(x, y) = 3x? + y³ at the point P(1,2) in the…

A:

Q: 40. (a) Let f(x, y, z) = x2 + y2 − xyz. Find grad f. (b) Find the equation for the tangent plane to…

A: