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1. Write two m-files, one for the bisection method and another for Newton's method.
2. Using both the Bisection method and the Newton method answer the following:
Include the commands you typed into Matlab
a) Find the root to 3, 5, and 8 decimal places of f(x) = x2- 2 starting with an initial approximation of x=1.
b) How many steps did it take for the bisection method to find the root to 3, 5, and 8 decimal places?
c) How many steps did it take for the Newton method to find the root to 3, 5 and 8 decimal places?
3. Use Newton's method to find all the real roots of f(x) = x5+ x4 -4x3 - 3x2- 3x +1
4. Apply Newton's method to the function f(x) = x3 - x with an initial approximation of x=1/√5. Is the method converging? What happens? Explain your answer using the graph of f(x).
5. Use Newton's method on the function (x) = 3√5 . What happens when your initial approximation is not x=0? Explain your answer using the graph of f(x).
Let's here start thinking regarding that how to solve nonhomogeneous differential equations. A second order, linear non-homogeneous differential equation is as y′′ + p (t) y′ +
what is the difference between North America''s part of the total population and Africa''s part
Q. Adding Fractions with the Same Denominator? Adding fractions with the same denominator is easy- you add the numerators (the tops), and you leave the denominator alone!
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Use the definition of the limit to prove the given limit. Solution Let ε> 0 is any number then we have to find a number δ > 0 so that the following will be true. |
The positive value of k for which x 2 +Kx +64 = 0 & x 2 - 8x + k = 0 will have real roots . Ans: x 2 + K x + 64 = 0 ⇒ b 2 -4ac > 0 K 2 - 256 > 0 K
Find the area of shaded region of circle of radius =7cm, if ∠AOB=70 o , ∠COD=50 o and ∠EOF=60 o . (Ans:77cm 2 ) Ans: Ar( Sector AOB + Sector COD + Sector OEF) = 7
Longer- Term Forecasting Moving averages, exponential smoothing and decomposition methods tend to be utilized for short to medium term forecasting. Longer term forecasting is
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Randi takes the stairs at work whenever possible instead of the elevator. She must climb up 51 steps from her office to get to the accounting department. The human resources depa
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