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Solving nonlinear equations 1. Programming: In this problem you will implement the 3 basic root?nding
algo- rithms discussed in class. For all three methods, your function should accept as inputs a function
name/ handle, two numbers which de?ne the initial bracket in- terval, a tolerance (1:01) and... 

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2. Finding roots: It is a very common strategy (used by many calculators) to calculate radicals of real
numbers using Newton's method (or similar methods). For example, the problem of calculating a: =
<75, can be reformulated as ?nding the roots of the function f (1:) = 3:3" ? a. In this probl... 

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3. Slow Newton's Method: From class, we know that Newton's method sometimes converges
quadratically, sometimes linearly, and sometimes not all. For this prob- lem, you will use your Newton
code to find one of the roots of f (1:) = 833(33 ? 1/2)3. (a) Find the positive root of the give... 

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4. Orders of Convergence: Consider the function ft?) = 85in3($) + $6 _ 21:4 _ $3 _ 1 on the interval [?2,
2]. This function has three roots. One root is r = 0, the others are difficult to find exact formulas for. (a)
Use Matlab's built in f zero function to find the other two roots. Use a tol- erance on the inp...