Find the linear approximation to the function | [z, y, z) = ze ºyz + 3x...
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).
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...
Q5. [8pnts] Use Taylor's formula to find a quadratic approximation of the function f(z, y) at the origin. Estimate the error in the approximation if |x| < .1 and |y| < .1 e-2y 1+n2 Q5. [8pnts] Use Taylor's formula to find a quadratic approximation of the function f(z, y) at the origin. Estimate the error in the approximation if |x|
Let f(x, y, z) = yln(zx) + ztan(xy). Find the linear approximation to f at the point (1,0,1). Use this linear approximation to approximate s(5,55 *). Show all of your work to obtain the linear approximation.
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) ≈ _______
Use a two-dimensional Taylor series to find a linear approximation for the function f (2,y) = sin (42) +y about the point (2,2).
write the equation of the line that represents the linear approximation to the following function at the given point a. answer a, b and c. a. Write the equation of the line that represents the linear approximation to the following function at the given point a b. Use the linear approximation to estimate the given quantity approximation - exact C. Compute the percent error in the approximation, 100. where the exact value is given by a calculator exact f(x) =...
a. Write the equation of the line that represents the linear approximation to the following function at the given point a. a. Write the equation of the line that represents the linear approximation to the following function at the given point a. b. Use the linear approximation to estimate the given quantity. approximation - exact| c. Compute the percent error in the approximation, 100. where the exact value is given by a calculator. |exact -0.04 f(x) = 3 e -*;...
(a) Suppose the equation defines a differentiable function y-f(z) (0) Find the derivatint ()-(e,l) (ii) Write the linear approximation for f(x) around a = e and use this to approx- dy Hence, e T,y 5 marks imate f(3). markS (b) Evaluate the following limits. Simplify your results if possible. 5 marks 5 marks] lim cot 5x sin 6x cos 7a (i) (ii) limIn (a) Suppose the equation defines a differentiable function y-f(z) (0) Find the derivatint ()-(e,l) (ii) Write the...