1. Locate a root of sin(x)=x2 where x is in radians. Use a graphical technique and...

1. Locate a root of sin(x)=x2 where x is in radians. Use a graphical technique and bisection with
the initial interval from 0.5 to 1. Perform the computation until ea is less than es=2%. Also
perform an error check by substituting your final answer into the original equation.
2. Determine the positive real root of ln(x
2
)=0.7 using three iterations of the bisection method,
with initial interval of [0.5:2].
3. Determine the lowest positive root of f(x)=7sin(x)e
-x
-1 using (a) the Newton-Raphson
method (three iterations, xi=0.3). (b) the secant method (five iterations, xi-1=0.5 and xi=0.4). (c)
the modified secant method (three iterations, xi=0.3, δ=0.01).
4. Use the Newton-Raphson method to find the root of f(x)=e
-0.5x
(4-x)-2. Employ initial guesses
of (a) 2, (b) 6, and (c) 8. Explain your results.

Expert Solution

Colby Messinger answered 8 months ago

sin(tan-1 x), where |x| < 1, is equal to: (a) x/√(1 – x2) (b) 1/√(1 – x2) (c) 1/√(1 + x2) (d) x/√(1 + x2)

sin(tan-1 x), where |x| < 1, is equal to:(a) x/√(1 – x²)(b) 1/√(1 – x²)(c) 1/√(1 + x²)(d) x/√(1 + x²)

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Find the Maclaurin series of f(x) = [sin(x2)]/x and find its radius of convergence.

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