Use the local linear approximation of f(x, y, z) = In(xz + y) at (2, -1, 1) to approximate f(1.98, –1.1, 1.02) O a. -0.139 Ob. -0.083 O c. -0.08 O d. -0.13

Q: find the linearization L(x, y) of the functionƒ(x, y) at the point P0 . Then find an upper bound for…

A: Given, f(x,y)=xy-3y2+2,   P0(1,1) Linearization of function at (a,b) is L(x,y)…

Q: Find the derivative of the function h (x, y, z) = cos xy+ e+ In zx %3D at P. (1, 0, 1/2), in the…

A: Here we have to find directional derivative of h(x,y,z) in the direction of u.

Q: Consider f(z, y) = Vzy+ 2y? ry- %3D Approximate f(2.4, 1.04) by using the tangent plane.

A: f(x,y)=xy+2y2

Q: Let F(x, y, z) = 6x?i – cos(xy)(i + 5). Calulate the divergence: div F(x, y, z) =

A:

Q: Evaluate the line integral [x(1 с where C is given by the line r(t) = (1 + 3t, 2t), 0≤ t ≤ 1. x(1 +…

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Q: Let y = 2x2 + 7x +3. If Aæ 0.3 at r 4, use linear approximation to estimate Ay %3D Ay 2 instructor

A: Linear approximation

Q: Find f(2, 1) and f(2.1, 1.05) and calculate Δz, and use the total differential dz to approximate Δz.…

A: Given

Q: U +2y at (0, 0) to estimate Use the linear approximation of f (x, y) = e3x²- f(-0.03, 0.03) =

A:

Q: Consider f(x, y) = x³y+ 2xy? Approximate f(2.1, 1.03) by using the tangent plane.

A: Given f(x, y) = x³y + 2xy² Find f(2.1, 1.03) using tangent plane.

Q: Use the chain rule to find dz/dt or dw/dt.  Z=sinxcosy, x=t^(-1/2) y=1/t

A: First of all, put x and y in the form of t and get the value of “z” in the form of “t” only.

Q: Evaluate the line integral F dr where F (x,y) - xy'i+ yj and the curve C is the shortest path from…

A:

Q: Let y = 3x + 3x + 2. If Aa = 0.4 at x = 1, use linear approximation to estimate Ay | Ay a

A: We have to find the change in y using linear approximation

Q: Use a local linear approximation of the function f(x) = VI cos[(V2x)T] approximate v3.98…

A:

Q: Consider z as a function of æ and y and z = Ax + By + D be the tangent plane to f(x, y) = 2a² + 2y³…

A:

Q: The task is to find the local linear approximation of V2 3 g(x,y) = +cot (x +5). TT at (1, –1) to…

A: Local linear approximation of f(x, y) at the point (a, b) is given by Lx,y=fa,b+fxa,bx-a+fya,by-b

Q: find the divergence of F. F(x,y) = √ +y I i+ Y Pa 꾸

A: F(x, y)=xx2+y2i+yx2+y2j

Q: Use chain rule to find dz/dt z=cos(x+2y), x=6t^3, y=7/t

A:

Q: Find the gradient of f(x, y, z) =e^y cos(xz) at (1,0,1) .

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Q: B) Evaluate the line integral F-dr. where F (x, y) = x*y²i+x²y°j and C is the curve r (t) = (t³ +…

A:

Q: 2. Let f(r) = v (2 - r)2. Use the local linear approximation of f (x) at ro = V0.99 (1.01)². 1 to…

A: Given Curve is f(x) =x2-x2  find linear approximation at x0=1  when x =0.99 value of f(x) at  x0=1…

Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = xy + yz + xz…

A: Function: f(x,y,z)=xy+yz+zx, at(0,0,0) We need to find fx,fy,fz. at the point (0,0,0)

Q: S F(2,v) For any function f(x, y) continuous on the ry-plane, f(r, y) dædy. O True False

A:

Q: Use a local linear approximation of the function f(z) = VI cos[(V2r)] at some approximate v3.98…

A: To use local linear approximation of the below function to approximate 3.98cos7.963π. fx=xcos2x3π

Q: Use the Chain Rule to find dz/dt. z = xy? - x?y, x = t2 + 1, y = t2 - 1 dz dt

A:

Q: Let L(r, y) = 2y – x + 3 be the local linear approximation to f(r,y) at (1,1) . Then f-(1,1) = %3D O…

A:

Q: Integrate f(x,y,z) = (x + y +z)/ (x² +y² +z? over the path r(t) =t i+tj+3t k, 0<a<t<b.

A:

Q: Consider the function: f(z,y) = 1 – xy coS TY (a) Find the linearization L(x, y) of ƒ at (1, 1) (b)…

A:

Q: Let z = g(x, y) = e* cos y + y ln(x – 1). Use local linear approximation to estimate g(1.99,0.01).…

A: Given Z(x,y)=g(x,y)=excosy+ylnx-1

Q: Determine the vactor feld of F. F(z, y) = yi - j

A: This is a problem related to vector field calculation. Based on the general concept we will provide…

Q: Use a parameterization R(u, v) of f (x,y) = xe*y to find the tangent plane to f(x, y) at the point…

A: Tangent plane at (x1, y1) to f(x, y) is given by below:

Q: B) Evaluate the line integral F-dr, where F (x, y) = x²y³i+ x°y°j and C is the curve r (t) = (t³ –…

A:

Q: 2. Let z = g(x, y) = e" cos y + y In(x – 1). %D Use local linear approximation to estimate g(1.99,…

A:

Q: Use the Linear Approximation off (x, y) = ex2+Y at (0, 0) to estimate f (0.01, -0.02). Compare with…

A: By the method of linear approximation, if we are given a differentiable function f in two variables,…

Q: Integrate f(x,y) =x+y over the curve C: x² + y = 49 in the first quadrant from (7,0) to (0,7).

A:

Q: If y (x, t) is a function of x and t, prove that i) Lat =py (x, p)- y (x, 0) ii) L- = p°y (x, p) –…

A:

Q: Find the differential of f(x, y) = Væ² +y8 at the point (1, 3). df = Then use the differential to…

A:

Q: Integrate f(x, y)= y cos xy over the rectangular 0 sxsm, 0 s ys 1*

A:

Q: Let F(x, y) = -o (a) + F. dr + j. Find the value of the line integral.

A: The general form of a vector-valued function in two dimensions is given by F=F1i+F2j, where F1 and…

Q: Use the Chain Rule to find dz/dt. z = xy9 − x2y,    x = t2 + 1,    y = t2 − 1

A:

Q: Using an appropriate linearization, the local linear approximation of is f(x) = T+ cos r at 2.

A:

Q: Find the direction of maximum change of f(x, y, z) = xey + z² at (1, In 2,2).

A: Introduction: A function's maximum directional derivatives at a particular point P are produced in…

Q: Using the Chain Rule, find dz/dt for z In(x? + y²) and x = t, y = t²

A:

Q: Using an appropriate linearization, the local linear approximation of f(z)= T+ sin z at 27 is

A:

Q: 4. Given f(x, y) = arctan(x + 2y). Find the local linear approximation of f at (1,0) and use it to…

A:

Q: Let z = g(x, y) = e² cos y + y ln(x – 1). | Use local linear approximation to estimate g(1.99,…

A: Here, z=g(x,y)=ex cos y+y ln (x-1) is the given function.

Q: x + Y f(x, y, z) = x sin + e*% – 1

A:

Q: 4x Estimate the error in the quadratic approximation of f(x,y) = e sin y at the origin over the…

A:

Q: Find f, for f(x, y) = | cos(r*) dt.

A:

Q: Integrate f(x, y) =x+y (4, 0) to (0, 4) over the curve C:x +y 16 in the first quadrant from %3D 32…

A:

Q: Set up the triple integral 8y dV, where E is bounded by the coordinate planes and the plane x + y +…

A: To Set up the triple integral for 8y dV, where E is bounded by the coordinate planes and the plane x…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.