A numerical algorithm approximates the value of sin(0.5) as 0.465. Note that is 0.5 radians. The...
A numerical algorithm approximates the value of sin(0.5) as 0.465. Note that is 0.5 radians. The true relative error (to 4 decimal places) in this approximation is
Homework Answers
Sin(0.5 radians) = sin(28.6478898∘)≈0.479425539
Relative error is given as:
(measured value - true value) / (true value)
= (0.465 - 0.479425539) / 0.479425539 = -0.0301
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A numerical algorithm approximates the value of sin(0.5) as
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the
question is from my Numerical methods and analysis course
et /()-sin(), where is measured in radians. (a). Calculate approximations to ) using Theorem 6.1 with h-0.1, h-0.01 and h-0.001, Carry eight or nine decimal places. (b). Compare with the value /(0.8)-cos(08), i.e. calculating the error of approximation. s(0.8) Theorem 6.1 (Centered Formula of Order 0(h)). Assume that fe Cla, bl and that x -h. x, x + h e la, bl. Then The notation S) stands for the set...
use radians in trig
functions
Estimate the slope f (3.5) for f(x)-sin(3xusing: a. Forward difference approximation with h 0.2 b. Backward difference approximation with h 0.2 c. Centered difference approximation with h 0.2. For each estimated slope, provide the true percent relative error, & Which approximation is the most accurate? Box your answ ers
An oscillating current in an electric circuit is described by
I=9e^-t sin(2pi*t). Determine all values of t such that I=3.5
From problem 6.18 in the book: Solve for the root using the bisection method, initial values x, = 0.35 and x, 0.45 and a stopping criterion &=0.5%. Start by rearranging the equation to set it up for root finding if I=3.5. Report your answers to 3 decimal places. Note: use radians for the sine component. iter xl eal (%) xu...
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h = 0.1
and then use
h = 0.05.
y' = y − y2, y(0) =
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