a) Use the Taylor theorem for function U(x, t) with the step size At. (x, is held constant) b) Consider the second-order truncation error (0(At )²) for the Taylor formula and then, obtain a finite difference approximation for the first-order derivative of U respect t ( U;(x,t)).

Q: b) Consider the second-order truncation error (0 (Ax)2) with the step size (-Ax) and then, obtain a…

A: The truncation error is O∆x2 and the step size is -∆x

Q: (7) (a) Find the linear approximation L(x, y) to the function f(x, y) = √² + y² + 4 at the point…

A:

Q: Consider the function g(x, y) = x² + xy + y² (1 + 1/2t, 2 + V3/2t), use the (a) Given the line l(t)…

A: Given,              g(x, y)=x2+xy+y2

Q: Let f(x) = r e-t dt – 1/2. Find root to f(r) by using bisection method. You should find the interval…

A: As the given integral is improper and have no closed form solution; we will use numerical…

Q: Find the second order Taylor approximation of the function f(x,y)=3e* sin y + 5x-2y near the point…

A: We are given that      f(x, y) = 3ex sin y + 5x - 2y   => f(0, 0) = 3e0 sin0 + 5×0 - 2×0 = 0…

Q: Let f(x,y) = ex/(1+y2) (a) Find a direction u such that Duf(0,1) = 0. (b) At which point(s) on the…

A:

Q: Find a linear approximation to f(x,y) : = (x? + y²)e-(x²+y*). At (0, 0), and use it to approximate…

A:

Q: (3) Consider the derivative dz = 2xydx + (x² + 2y)dy Evaluate whether this is a total derivative, by…

A: We will check whether the given function is total derivative or not. We also integrate dz pathwise.

Q: The minimum rate of change of the function f(x, y) = In(x² + y²) at the point (-1,0) is: a. -1 O b.…

A:

Q: 3) a) Use the Taylor theorem for function U(x, t) with the step size(-Ax) (t, is held cons. b)…

A:

Q: Consider the function:  f (x,y) = -x2 + 2xy + 2x + y2 - 6y + 1  Find the maximum rate of increase…

A: It is given that fx,y=-x2+2xy+2x+y2-6y+1. The objective is to evaluate the directional derivative at…

Q: 3. Find the derivative of the function f(r, y, ) = xy + yz+ the direction A = 3i + 6j – 2k. zr at…

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Q: The direchional derivative of the salan funchion at (l,-1,0) in the direction (i-j+2k) is xy- z- xyz…

A: Given that  Let f(x,y,z)=x^2y-y^2z-xyz To find the directional derivative at point

Q: Find all the first and second order derivatives of the function f(x, y) = x³ ln(y) + xy + x³y² + 4x…

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Q: 1. Let F(t) = (e¹−¹ – ť², 3t² + 1, 4-5 lnt), G(1) = (-6, 1,0), and f(t) = cost. Evaluate: (a) (F-G)…

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Q: Let f(1,y) = (r+ay°,r²y°,2r + by), g(u, v,w) = (3u² + bv² + w°, uvw). Find the derivative of…

A: Let f(x, y)=x3+ay2, x2y3, 2x+by,  gu, v, w=3u2+bv2+w3, uvw. We need to find the derivative of fgu,…

Q: Let f(x)= sec(x), find the linear approximation at x= pi/4 and use it to estimate sec(pi/5)

A: Given function: fx=secx At x=π4 fπ4=secπ4=2

Q: ) Find an analytic function f(z) = u(xr, y) + iv(r, y) with real part -. -----) u(r, y) = x? – y? +…

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Q: 3) a) Use the Taylor theorem for function U(x, t) with the step size(-Ax) (t, is held cons. b)…

A: