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Q5. [8pnts] Use Taylor's formula to find a quadratic approximation of the function f(z, y) at the origin. Estimate...
Q5. [8pnts] Use Taylor's formula to find a quadratic approximation of the function f (x, 3) e-2y 1+22-y HE2-7 at th...
Q5. [8pnts] Use Taylor's formula to find a quadratic approximation of the function f (x, 3) e-2y 1+22-y HE2-7 at the origin. Estimate the error in the approximation if ㈣く.1 and lyl < .1.
Q5. [8pnts] Use Taylor's formula to find a quadratic approximation of the function f (x, 3) e-2y 1+22-y HE2-7 at the origin. Estimate the error in the approximation if ㈣く.1 and lyl
Quadratic approximation: Cubic approximation: 2 near the origin Use Taylor's formula for f(x,y) at the origin...
Quadratic approximation:
Cubic approximation:
2 near the origin Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approximations of f(x,y) = 7- x-V The quadratic approximation for f(x,y) is
2 near the origin Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approximations of f(x,y) = 7- x-V The quadratic approximation for f(x,y) is
14.7. Taylor's theorem and Max/Min values. A statement of Taylor's theorem for functions of two variables...
14.7. Taylor's theorem and Max/Min values. A statement of Taylor's theorem for functions of two variables and an example are in Part I (section 7) of my online notes if you didn't get it in class. H. Compute the Hessian of the function f(x,y) = y?e evaluated at the point (0,2), ans (lo 8 I. Use the formula involving the gradient and Hessian for z = Q(x, y) to determine the second order Tavlor polynomial for the functions. You should...
7. Find the linear approximation of f(x,y)=-x’ +2y’ at (3,-1) and use this approximation to estimate...
7. Find the linear approximation of f(x,y)=-x’ +2y’ at (3,-1) and use this approximation to estimate f(3.1.-1.04). S (3,-1) = (3.-1) = ,(3,-1) = L(x, y)= L(3.1, -1.04) =
Σπ . If we use the quadratic Maclaurin polynomial of ex 12. (2 pts) Recall that ez to estimate Ve, use Taylor's Remainder Theorem to find a bound on the error of this estimate. Σπ . If w...
Σπ . If we use the quadratic Maclaurin polynomial of ex 12. (2 pts) Recall that ez to estimate Ve, use Taylor's Remainder Theorem to find a bound on the error of this estimate.
Σπ . If we use the quadratic Maclaurin polynomial of ex 12. (2 pts) Recall that ez to estimate Ve, use Taylor's Remainder Theorem to find a bound on the error of this estimate.
a. Find the linear approximation for the following function at the given point. b. Use part...
a. Find the linear approximation for the following function at the given point. b. Use part (a) to estimate the given function value. f(x,y) = 3x - 2y + 8xy; (3,5); estimate f(2.9,5.02) a. L(x,y)= b. L(2.9,5.02) = (Type an integer or a decimal.)
2. Suppose the linear approximation of a differentiable function f(x, y, z) at the point (1,2,3)...
2. Suppose the linear approximation of a differentiable function f(x, y, z) at the point (1,2,3) is given by L(x, y, z) = 17+ 6(x – 1) – 4(y – 2) + 5(2 – 3). Suppose furthermore that x, y and z are functions of (s, t), with (x(0,0), y(0,0), z(0,0)) = (1, 2, 3), and the differentials computed at (s, t) = (0,0) are given by dx = 7ds + 10dt, dy = 4ds – 3dt, dz = 2ds...
1. 2. (1 point) Let f(x,y,z) = 4x2 + xy + yz +5z?. Find the linearization...
1.
2.
(1 point) Let f(x,y,z) = 4x2 + xy + yz +5z?. Find the linearization L(x, y, z) of f(x,y,z) at the point (-1, -3, -1). L(x,y,z) = -5x-2y+72-3 Find an upper bound for the magnitude El of the error in the approximation f(x, y, z) ~ L(x, y, z) over the box |x +11 30.04, \y +31 < 0.04, 12 +11 30.04. E 3 (1 point) Let f(x, y) = 3 In(x) +2 In(y). Find the linearization L(av)...
Please explain b! 2. Let z = f(x, y) = ln(4x2 + y2) (a) Use a...
Please explain b!
2. Let z = f(x, y) = ln(4x2 + y2) (a) Use a linear approximation of the function z = f(x,y) at (0,1) to estimate f(0.1, 1.2) (b) Find a point P(a,b,c) on the graph of z = f(x, y) such that the tangent plane to the graph of z = f(x,y) at the point P is parallel to the plane 2x + 2y – 2=3
Find the linear approximation to the function | [z, y, z) = ze ºyz + 3x...
Find the linear approximation to the function | [z, y, z) = ze ºyz + 3x at the point (2, 4, z) = (1, -3,0) I (2,4.2) = write the appropriate function of 2.yand :). OS Use this linear approximation to estimate (0.95.3.1,0.05) Number the numerical answer must be precise up to 2001
Q5. [8pnts] Use Taylor's formula to find a quadratic approximation of the function f (x, 3) e-2y 1+22-y HE2-7 at the origin. Estimate the error in the approximation if ㈣く.1 and lyl < .1.
Q5. [8pnts] Use Taylor's formula to find a quadratic approximation of the function f (x, 3) e-2y 1+22-y HE2-7 at the origin. Estimate the error in the approximation if ㈣く.1 and lyl
Quadratic approximation:
Cubic approximation:
2 near the origin Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approximations of f(x,y) = 7- x-V The quadratic approximation for f(x,y) is
2 near the origin Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approximations of f(x,y) = 7- x-V The quadratic approximation for f(x,y) is
14.7. Taylor's theorem and Max/Min values. A statement of Taylor's theorem for functions of two variables and an example are in Part I (section 7) of my online notes if you didn't get it in class. H. Compute the Hessian of the function f(x,y) = y?e evaluated at the point (0,2), ans (lo 8 I. Use the formula involving the gradient and Hessian for z = Q(x, y) to determine the second order Tavlor polynomial for the functions. You should...
7. Find the linear approximation of f(x,y)=-x’ +2y’ at (3,-1) and use this approximation to estimate f(3.1.-1.04). S (3,-1) = (3.-1) = ,(3,-1) = L(x, y)= L(3.1, -1.04) =
Σπ . If we use the quadratic Maclaurin polynomial of ex 12. (2 pts) Recall that ez to estimate Ve, use Taylor's Remainder Theorem to find a bound on the error of this estimate.
Σπ . If we use the quadratic Maclaurin polynomial of ex 12. (2 pts) Recall that ez to estimate Ve, use Taylor's Remainder Theorem to find a bound on the error of this estimate.
a. Find the linear approximation for the following function at the given point. b. Use part (a) to estimate the given function value. f(x,y) = 3x - 2y + 8xy; (3,5); estimate f(2.9,5.02) a. L(x,y)= b. L(2.9,5.02) = (Type an integer or a decimal.)
2. Suppose the linear approximation of a differentiable function f(x, y, z) at the point (1,2,3) is given by L(x, y, z) = 17+ 6(x – 1) – 4(y – 2) + 5(2 – 3). Suppose furthermore that x, y and z are functions of (s, t), with (x(0,0), y(0,0), z(0,0)) = (1, 2, 3), and the differentials computed at (s, t) = (0,0) are given by dx = 7ds + 10dt, dy = 4ds – 3dt, dz = 2ds...
1.
2.
(1 point) Let f(x,y,z) = 4x2 + xy + yz +5z?. Find the linearization L(x, y, z) of f(x,y,z) at the point (-1, -3, -1). L(x,y,z) = -5x-2y+72-3 Find an upper bound for the magnitude El of the error in the approximation f(x, y, z) ~ L(x, y, z) over the box |x +11 30.04, \y +31 < 0.04, 12 +11 30.04. E 3 (1 point) Let f(x, y) = 3 In(x) +2 In(y). Find the linearization L(av)...
Please explain b!
2. Let z = f(x, y) = ln(4x2 + y2) (a) Use a linear approximation of the function z = f(x,y) at (0,1) to estimate f(0.1, 1.2) (b) Find a point P(a,b,c) on the graph of z = f(x, y) such that the tangent plane to the graph of z = f(x,y) at the point P is parallel to the plane 2x + 2y – 2=3
Find the linear approximation to the function | [z, y, z) = ze ºyz + 3x at the point (2, 4, z) = (1, -3,0) I (2,4.2) = write the appropriate function of 2.yand :). OS Use this linear approximation to estimate (0.95.3.1,0.05) Number the numerical answer must be precise up to 2001
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