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Given the function: f(x) x2 + 4x + et and the point f(1)...
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...
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...
MATLAB 1) Calculate the following for the function f(x) = e-4x- 2x3
#use MATLAB script1) Calculate the following for the function f(x) = e-4x- 2x3 a. Calculate the derivative of the function by hand. Write a MATLAB function that calculates the derivative 05. of this function and calculate the derivative at x = 0.5. b. Develop an M- to evaluate the cetered finite-difference approximation (use equation below), at x = 0.5. Assume that h = 0.1. c. Repeat part (b) for the second-order forward and backward differences. Again Assume that h = 0.1. d. Using the results...
(1 point) Consider the function f(x) = x2 - 4x + 2 on the interval [0,4]....
(1 point) Consider the function f(x) = x2 - 4x + 2 on the interval [0,4]. Verify that this function satisfies the three hypotheses of Rolle's Theorem on the inverval. on f(x) is on [0, 4); f(x) is (0, 4); and f(0) = f(4) = Then by Rolle's theorem, there exists at least one value c such that f'(c) = 0. Find all such values c and enter them as a comma-separated list. Values of се (1 point) Given f(x)...
Please write neat and show work/steps 3. Consider the function f(x) = (4x +5 on the...
Please write neat and show work/steps
3. Consider the function f(x) = (4x +5 on the interval (-1.1). (a) Find the quadratic Taylor approximation fr(x) > 00 + 10 + c2x2. Calculate the C to four decimal places. (b) Find the quadratic Legendre approximation f1(x) -- 20 +ajx + a2x?. Calculate the a; to four decimal places. If the two approximations differ greatly, something is probably wrong. You may want to consult section 4 in the pdf I sent you...
Let f be the function defined by f(x) = 12 exp(x2 – 3x). The function exp(u)...
Let f be the function defined by f(x) = 12 exp(x2 – 3x). The function exp(u) is another name for e". a) Find L(x) the linear approximation to f at 3. L(x) = help (formulas) b) Use the Linear Approximation for f(x) = 12 exp(x2 – 3x) at 3 to estimate f(3.08). f(3 + 0.08) help (decimals). c) Find the error in the linear approximation to the value of f(3 + 0.08) that we found in part b). The error...
(1 point) Find the linearization of the function f(x,y) = 72 - 4x² – 2y at...
(1 point) Find the linearization of the function f(x,y) = 72 - 4x² – 2y at the point (3, 4). L(x,y) Use the linear approximation to estimate the value of f(2.9, 4.1) f(2.9, 4.1)
Compute a FD second order approximation of the first derivative of the function f(x) = sin(x2) at...
Compute a FD second order approximation of the first derivative of the function f(x) = sin(x2) at x = 1.5 using x = 0.1
3. Consider the function f(x) = 4x + 5 on the interval [-1.1]. (a) Find the...
3. Consider the function f(x) = 4x + 5 on the interval [-1.1]. (a) Find the quadratic Taylor approximation fr(x) = co + Cl2 + 22x2. Calculate the Ci to four decimal places. (b) Find the quadratic Legendre approximation fl(x) = do + 01x + 22x. Calculate the ai to four decimal places. If the two approximations differ greatly, something is probably wrong. You may want to consult section 4 in the pdf I sent you on orthogonal polynomials.
Please use matlab to solve the question. 1. The following infinite series can be used to...
Please use matlab to solve the question.
1. The following infinite series can be used to approximate e*: 2 3! n! Prove that this Maclaurin series expansion is a special case of the Taylor series (Eq. 4.13) with Xi = 0 and h a) x. b) Use the Taylor series to estimate f(x) e* at xH1 1 for x-0.25. Employ the zero-, first-, second- and third-order versions and compute the letlfor each case. Take the true value of e10.367879 for...
c) Using Matlab function "fmincon", find the maximum and minimum of the function f(x, y) 4x...
c) Using Matlab function "fmincon", find the maximum and minimum of the function f(x, y) 4x + 3y g(x,y) x2 +y2 100
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...
(1 point) Consider the function f(x) = x2 - 4x + 2 on the interval [0,4]. Verify that this function satisfies the three hypotheses of Rolle's Theorem on the inverval. on f(x) is on [0, 4); f(x) is (0, 4); and f(0) = f(4) = Then by Rolle's theorem, there exists at least one value c such that f'(c) = 0. Find all such values c and enter them as a comma-separated list. Values of се (1 point) Given f(x)...
Please write neat and show work/steps
3. Consider the function f(x) = (4x +5 on the interval (-1.1). (a) Find the quadratic Taylor approximation fr(x) > 00 + 10 + c2x2. Calculate the C to four decimal places. (b) Find the quadratic Legendre approximation f1(x) -- 20 +ajx + a2x?. Calculate the a; to four decimal places. If the two approximations differ greatly, something is probably wrong. You may want to consult section 4 in the pdf I sent you...
Let f be the function defined by f(x) = 12 exp(x2 – 3x). The function exp(u) is another name for e". a) Find L(x) the linear approximation to f at 3. L(x) = help (formulas) b) Use the Linear Approximation for f(x) = 12 exp(x2 – 3x) at 3 to estimate f(3.08). f(3 + 0.08) help (decimals). c) Find the error in the linear approximation to the value of f(3 + 0.08) that we found in part b). The error...
(1 point) Find the linearization of the function f(x,y) = 72 - 4x² – 2y at the point (3, 4). L(x,y) Use the linear approximation to estimate the value of f(2.9, 4.1) f(2.9, 4.1)
3. Consider the function f(x) = 4x + 5 on the interval [-1.1]. (a) Find the quadratic Taylor approximation fr(x) = co + Cl2 + 22x2. Calculate the Ci to four decimal places. (b) Find the quadratic Legendre approximation fl(x) = do + 01x + 22x. Calculate the ai to four decimal places. If the two approximations differ greatly, something is probably wrong. You may want to consult section 4 in the pdf I sent you on orthogonal polynomials.
Please use matlab to solve the question.
1. The following infinite series can be used to approximate e*: 2 3! n! Prove that this Maclaurin series expansion is a special case of the Taylor series (Eq. 4.13) with Xi = 0 and h a) x. b) Use the Taylor series to estimate f(x) e* at xH1 1 for x-0.25. Employ the zero-, first-, second- and third-order versions and compute the letlfor each case. Take the true value of e10.367879 for...
c) Using Matlab function "fmincon", find the maximum and minimum of the function f(x, y) 4x + 3y g(x,y) x2 +y2 100
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