24.9 and 25.1. Find the local linear approximation of the function f(x) = V14 + x...
Exam 2018s1] Consider the function f R2 R, defined by f(x,y) =12y + 3y-2 (a) Find the first-order Taylor approximation at the point Xo-(1,-2) and use it to find an approximate value for f(1.1,-2.1 (b) Calculate the Hessian 1 (x-4)' (Hr(%)) (x-%) at X-(1-2) c) Find the second-order Taylor approximation at xo- (1,-2) and use it to find an approximate value for f(1.1,-2.1 Use the calculator to compute the exact value of the function f(11,-2.1) Exam 2018s1] Consider the function...
Question 6 (2 marks) Not yet answered Find the linear approximation of f(x) = el-* at x = 1 Use the linear approximation to approximate the value of 0.1 and compare it to its exact value. Explain why you can use the linear approximation to estimate eº-1 with high accuracy but not e-4 Marked out of 6.00 (4 marks) Flag question B 32 U X x2 lll E E 23T
3. (8 points) Find an appropriate local linear approximation for the function cos(x) and estimate the value of cos 31°.
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)
(3 points) The figure shows how a function f (x) and its linear approximation (.e., its tangent line) change value when I changes from co to co + dr. y = f(x) fredr) Suppose f(x) = x2 + 2x, xo = 2 and dr = 0.05. Your answers below need to be very precise, so use many decimal places. (a) Find the change Af = f (30+ dc) - f(:30). Af Error = 14f-df Af = f(x + dr) -...
(a) (b) Find the least squares approximation of f(x) = x2 + 3 over the interval [0, 1] by a function of the form y = ae? + bx, where a, b E R. You should write the coefficients a, b as decimal approximations, rounded to two decimal places. Let g(x) be the least squares approximation you found in the pre- vious problem. So g(x) = ae” + bx for some scalars a, b. Find the least squares approximation of...
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) ≈ _______
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) =...
Given the function below f(x) = 3 – 45x3 + 72 Find the equation of the tangent line to the graph of the function at x = 1. Answer in mx + b form. L(x) Use the tangent line to approximate f(1.1). L(1.1) Compute the actual value of f(1.1). What is the error between the function value and the linear approximation? Answer as a positive value only. error (Approximate to at least 5 decimal places.)
CALCULUS Consider the function f : R2 → R, defined by ï. Exam 2018 (a) Find the first-order Taylor approximation at the point Xo-(1, -2) and use it to find an approximate value for f(1.1, -2.1 (b) Calculate the Hessian ã (x-xo)' (H/(%)) (x-xo) at xo (1,-2) (c) Find the second-order Taylor approximation at Xo (1,-2) and use it to find an approximate value for f(1.1, -2.1) Use the calculator to compute the exact value of the function f(1.1,-2.1) 2....