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Find the linear approximation of given function at (0,0). 5.r + 2 f (x,y) 5y +...
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...
Find the linear approximation to the function f (,y) = 34+ 3xy at the point (2,y) = (3,-1). L 2,y) = (write the appropriate function of u and y). Use this linear approximation to estimate f (3.03, -1.02) Number (the numerical answer must be precise up to +0.001).
Exercice 2 (5pts) Let f given by f(x, y) Isinyif (x, y) (0,0) and f(0,0) 0 1V224 1. Is f continuous at (0,0). 2. Compute the partial derivatives of f at any (x, y) E R2. Are the partial derivatives continuous (0,0). at (0,0) (0,0) and 3. Compute the second derivatives 4. Compute the linear approzimant of f at (0,0). Exercice 2 (5pts) Let f given by f(x, y) Isinyif (x, y) (0,0) and f(0,0) 0 1V224 1. Is f...
Find the linear approximation of the function below at the indicated point. f(x,y) = In(x - 4y) at (9,2) f(x, y) ≈ _______ Use the approximation to find (8.91, 2.04), (Round your answer to three decimal places.) f(8.91, 2.04) ≈ _______
7. Find the linear approximation of the function f(x,y) = ery at (1,0) and use it to approximate f(0.9.0.1). (6 Pts)
2. Consider the function f : R2 → R defined below. r3уг_ if (x,y) (0,0) f(x,y) = if (x, y) (0, 0) (a) Prove that f is continuous at (0,0) (b) Calculate the partial derivatives (0,0) and (0,0) directly from the definition of partial derivatives. (c) Prove that f is not differentiable at (0,0).
1. Linear Approximations. a. (40 pts) Find the linear approximation L(x) to the function f(x)tan(rx) at a (20 pts) Use the linear approximation to determinethe value at x = 0.4 at χ = 0.4, Compute the relative error: Then compare f(x) and L(x) LLarrul × 100% 1f(x)1 r(x)l 1. Linear Approximations. a. (40 pts) Find the linear approximation L(x) to the function f(x)tan(rx) at a (20 pts) Use the linear approximation to determinethe value at x = 0.4 at χ...
Given the function f(r.y) lim f(x, y) (ry)-+(0,0) a. Evaluate iii. Along the line y= r: i. Along the r-axis: iv. Along y12 ii. Along the gy-axis: ,f(x, y) exist? If yes, find the limit. If no, explain why not. lim (a.)-(0,0) b. Does (0,0)? Why or why not? c. Is f continuous at d. The graphs below show the surface and contour plots of f (graphed using WolframAlpha). Explain how the graphs explain your answers to parts (a)-(c) above....
1. Find the absolute maximum and minimum values of f(r,y) = x2+y2+5y on the disc {(x, y) | x2+y2 < 4}, and identify the points where these values are attained 2. Find the absolute maximum and minimum values of f(x, y) = x3 - 3x - y* + 12y on the closed region bounded by the quadrilateral with vertices at (0,0), (2,2), (2,3), (0,3), and identify the points where these values are attained. 3. A rectangular box is to have...
7. (5 points) Find the linear approximation for f(x) = tan(2x) at a = 0 and use it to approximate the value of tan(0.002). Hint: The linear approximation is just the tangent line to the curve at a = 2. 8. (5 points) Use the Mean Value Theorem for derivatives to find the value of x = c for f(x) = Vx on the interval (1,9). 9. (5 points) The acceleration of an object moving along the number line at...