Let L(x, y) = y- x+ 3 be the local linear approximation to f(æ, y) at (1, 1) .Then f(1, 1)%3D a. 3. O b. -1 Oc. O d. -3 e. -2 O f. 2 Ouestion 2 Compaq 6820s

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: Let y = 2x + 7x +3. If Ax = 0.3 at x = 4, use linear approximation to estimate Ay Ay 2

A: Linear approximation

Q: 2. Evaluate the given line integral, | (-y,x – y) · dR, where C is the line segment from (1,0) to…

A: To find the line integral we use the equation of line segment in parametric form using given points.

Q: Compute Scy dx + xy dy if C goes from (0,0) to (1,2) along the line parameterized as x = t, y = 2t.

A:

Q: Assume that x and y are functions of t. If y = x² + 4x and dx/dt = 4, find dy/dt when x = 1. dy dt…

A: Solve the following

Q: fo F(1+ 2t, 1+ 3t)dt is equivalent to the line integral of F(x, y) on the line segment from (1,1) to…

A: Here we have to find is the given statement is true or false

Q: Let y = 5x? + 5a + 3. If Aæ = 0.3 at x = 4, use linear approximation to estimate Ay Ay = > Next…

A: Explanation of the answer is as follows

Q: Use the local linear approximation of f(x, y, z) = In(xz + y) at (2, -1, 1) to approximate f(1.98,…

A:

Q: Integrate h (x. y) xy'i+2j over the indicated path: Brr(u) = (1- u)i. HE [0. 2).

A: Consider the given function and path.

Q: 2. Evaluate the given line integral, (-y,x – y) · dR, where C is the line segment from (1, 0) to…

A: Introduction: The formula of line integral of the function f(x,y) on the line segment C(t) is given…

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

A: Topic:- partial differentiation

Q: If F = xi + -4yj +x2k determine the flux of F through S, where S is the portion of z2 = x2 + y2,…

A: Given - F = x i^ - 4y j^ + x2 k^  ;             S is the portion of z2 = x2 +y2 , 1 ≤ z ≤ 3 To find…

Q: 0.1 at c 5, use linear approximation to estimate Ay Let y 2x + 8x + 4. If Ar Ay =

A:

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: (b) 6xy dV, where E lies under the plane z=1+x+y and above the region in the xy-plane bounded by the…

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

Q: Let y = 5x² + 8x + 4. If Ax = 0.4 at x = 2, use linear approximation to estimate Ay Ay a

A: By linear approximation we can write,       ∆y ≈ dy = f'(x) dx Also We have,          ∆y =…

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: a) Evaluate ff, (3 – 4x)dV where E is the region below z = 4 – xy and above the region in xy – plane…

A: To evaluate the given triple integral.

Q: Compute d/dt f (r(t)) at the given value of t for f (x, y, z) = xz − y^2, r(t) =〈t, t^3, 1 − t〉at t…

A: Given: The function fx,y,z=xz-y2and rt=t,t2,1-t, To find: ddtfrt at t=-2,

Q: 2. Evaluate the given line integral, (x – y, y) · dR, where C is the line segment from (0, 1) to…

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

A:

Q: Let y = 4x2 + 7x + 4. If Az = 0.2 at z 4, use linear approximation to estimate Ay Ay s

A:

Q: Given r(t)=t i+2t j and 0 <t< 1. Evaluate the line integral f,(x+y) ds = fr(1)r'(1) dt. a

A:

Q: Evaluate x*dx C + xy dy, where C is the triangular curve consisting of the line segments from (0, 0)…

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: Let f(x, y, z) = x² + 2y+ e³=2« + 2°. Find the rate at which f is changing at (1,2, –1) in the…

A: Use the formula of the directional derivative and simplify.

Q: If L(x, y) is the local linear approximation of f(x, y)= x²+2y3+ 9:" at (2, 1) where g(2, 1) = 4,…

A: Given: f(x,y)=x2+2y3+g(x,y)x g(2,1)=4 gx(2,1)=4 gy(2,1)=6 At (2,1).…

Q: Evaluate the line integral cy dx + x dy where C is the parameterized path x = y = t° , 2<t< 6. Scydx…

A:

Q: Let y = 5x + 2x +3. If Ax = 0.1 at x = 3, use linear approximation to estimate Ay %3D Ay 2 Ouestion…

A: We have to find

Q: a) Evaluate the line integral S. (2x – y) dx – (x + 3y) dy, where C is a straight line from (1,1) to…

A:

Q: 2. Evaluate the given line integral, (-y,x – y) · dR, where C is the line segment from (1,0) to…

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: Let y = 5x + 4c +3. If Ar 0.1 at z 5, use linear approximation to estimate Ay

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: Let y 522 + 2x + 3. If Aæ = 0.4 at x = 3, use linear approximation to estimate Ay Ay =

A:

Q: If C is any sectionally smooth curve, which of the following line integrals is NOT path-independent?…

A:

Q: Assume x and y are functions of t. Evaluate dy / dt for the following. y3 = 2x 4 + 6 ;        dx /…

A:

Q: Let y = 4a2 + 8x + 2. If Aæ 0.4 at x = 5, use linear approximation to estimate Ay %3D %3D Ay =

A:

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

A:

Q: Let y 5x? + 4x + 3. If Ar 0.1 at I = 5, use linear approximation to estimate Ay

A:

Q: Let y = 3z? + 6z + 4. If Ar = 0.4 at z = 3, use linear approximation to estimate Ay %3D Ay = Preview

A:

Q: Assume that w= f(s° +t*) and f'(x) = e*. Find and dt D I3D 次咖一。

A: Finding the expression of w and proceed the differentiation

Q: assume x and y are functions of t.  Evaluate dy/dt for the following: y3=2x4+6; dx/dt=2, x=1, y=2

A: The given function is  y3 = 2x4 + 6    ...... (1) dx/dt = 2, x = 1,   y = 2

Q: Show that F(x, y, z) = (y² – e* sin z)i + (2xy + z)j + (y – e* cos z)k is conservative and hence…

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: Evaluate the line integral ſ. 3(x – y) ds along the path C:r(t) = ti + (2 - t)j, 0<t<1

A:

Q: Use Green's Theorem to evaluate (e" + y²) dx+ (e" +x²) dy where C is the boundary of the region…

A: we have to evaluate the following by using greens theorem