Find the Taylor polynomial of degree 2 centered at a = 1 for the
function f(x) = e^(2x) . Use Taylor’s Inequality to estimate the
accuracy of the approximation e^(2x) ≈ T2(x) when 0.7 ≤
x ≤ 1.3
Consider the polynomial f(x) = 3x 3 + 5x 2 − 58x − 40. Using
MATLAB. Find the three roots of the polynomial, i.e, x where f(x) =
0, using Newton’s method. Report the number of iterations taken by
each algorithm using a tolerance of 10−8 .
Using MATLAB, Consider the polynomial f(x) = 3x^3 + 5x^2 − 58x −
40. Find the three roots of the polynomial, i.e, x where f(x) = 0,
using: (i) Bisection method, and (ii) Newton’s method. Report the
number of iterations taken by each algorithm using a tolerance of
10^−8 .
Use the Lagrange interpolating polynomial to approximate √3 with the function f(x)= 3x-0.181and the values x0=-2, X1=-1, X2=0, X3=1 and X4=2.(Uses 4 decimal figures)
consider the function f(x) = 1 +
x3 e-.3x
a. what is f'(x)
b. what is f''(x)
c. what are the critical points of f(x)
d. are the critical points a local min or local max or
neither?
e. find the inflection points
f. if we define f(x) to have the domain of [2,50] compute the
global extreme of f(x) on that interval
-- Find the linear approximation of the function f(x,y)= e^(x^2 + 4xy - 2y^2) at (1,2) using the aproximate f(0.99,2.01)
-- find Zvu for z= f(x,y), x=uv , y= v^2 + u^2
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