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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).
Tangents with Polar Coordinates Here we now require to discuss some calculus topics in terms of polar coordinates. We will begin with finding tangent lines to polar curves.
prove that sin A /cot A + cosec A = 2 + sinA / cot A - cosec A
what is the business application of matrices
Reasons why we start division : The reason we start division by considering the digit in the leftmost place is efficiency and ease . For instance, suppose we divide 417 by 3, we
Mathematical Formulae (a + b) 2 = a 2 + b 2 + 2ab (a - b) 2 = a 2 + b 2 - 2ab (a + b) 2 +
evaluate limit as x approaches 0 (x squared times sin (1/x)
A real estate agent makes a 1.5% commission on her sales. What is her commission if she sells a $359,000 house? Multiply $359,000 by the decimal equivalent of 1.5% (0.015) to ?
3. How are Indian customers visiting Shoppers’ Stop any different from customers of developed western countries? 4. How should Shoppers’ Stop develop its demand forecasts?
20+20
Here we look at only the rules without going into their proofs. They are: a 0. If a If a If a
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