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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).
If f(x) is an infinitely differentiable function so the Taylor Series of f(x) about x=x 0 is, Recall that, f (0) (x) = f(x) f (n) (x) = nth derivative of f(x)
#qu Given the equation through what angle should the axes be rotated so that the term in xy be waiting from the transformed equation. estion..
if you have 1/5 of a candy bar and 4 friends how much will they get
The curve (y+1) 2 =x 2 passes by the points (1, 0) and (- 1, 0). Does Rolle's Theorem clarify the conclusion that dy dx vanishes for some value of x in the interval -1≤x≤1?
how to work out inequalities with negative signs?
Evaluate the given limits, showing all working: Using first principles (i.e. the method used in Example 1, Washington 2009, Using definition to find derivative ) find the
Find the relation between x and y when the point (x,y) lies on the straight line joining the points (2,-3) and (1,4) [ Hint: Use area of triangle is 0] Ans : Hint: If the poi
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Verify Liouville''''s formula for y "-y" - y'''' + y = 0 in (0, 1) ?
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