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- 2) Find the root of the polynomail f(x)= x' – 3 x² +2 by using the Newton's Method. You must do at least three iterations and confirm your answer to see if the root evaluates close to zero3. Consider the equation f(x) = x³ - 2x² – 11x + 12 on the interval [1.78, 8.25]. (a) Find the minimum number of iterations required to find the root of the given equation within the error bound of 1 x 10-3. (b) Show 5 iterations using the Bisection Method to find the root of the above function within the interval [1.78, 8.25].Find the minimal polynomial that will approximate the function F(x) with an error of magnitude e < 10-3 throughout the interval [0, 1]. F(x) = | sint dt Justify your reasoning.
- 3- Verify the MVT with f (x) = √√7x, a=1 and b=16.2. Find all critical numbers for the function: g(x) = xv2x +1 1 A. -- 0, 글, 글 А. В. -- 3 2 2 1 С. 3 1 1 D. - -- - 2 3For f(x)=12x" – 44xr' - 8x° + 2x' – 6x’ + 72x² – 24.x+8 , compute f(2), roots of f(x) and plot for 0The false-position method may have difficulty in finding the root of f(x) = x² - 7.4x + 13.69 0 because Of(x) is a quadratic polynomial O the equation has two identical roots. O f'(x) is a straight line one cannot find initial guesses and xy that satisfy ƒ(x₁) ƒ (xv) < 010. Consider the function f(x) = x³ + 2x² + 10x - 20 = 0 1. Show that f(x) has one single root in the interval ]1, 2[ 2. Show that this function can be put into the form: x = 3. Show that for a root in the interval re [1,2]: F'(r)| ≤ // 4. Find the root of f(x) in the interval [1, 2] F(x) = ²+bx+c 3m1Find the root of the function f(x) = e-x- x using Newton-Raphson Method. (Please include the table with iteration, xi, xi+1, f(xi+1), f(xi+1), xr, f(xr) and f(xi)f(xr)Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,