MAE 284 Exam 1 Questions & Answers 2024/2025
Bracketing Methods always require two initial estimates (T/F) - ANSWERSTrue
Discontinuous functions can result in a bracket with opposite sgned function values having an even number of root (T/F) - ANSWERSTrue
Bracketing methods always converg...
Bracketing Methods always require two initial estimates (T/F) - ANSWERSTrue
Discontinuous functions can result in a bracket with opposite sgned function values having an even
number of root (T/F) - ANSWERSTrue
Bracketing methods always converge, but usually do so more slowly than open methods (T/F) -
ANSWERSTrue
The secant method is similar to the Newton-Raphson method, but uses an approximation of the
derivative (T/F) - ANSWERSTrue
MATLAB's built in fzero function is based on the Newton-Raphson method (T/F) - ANSWERSFalse
Suppose you are given the [a,b]= mae284(p,q,r,s) and the user doesn't specify the inpt value for 's',
which line of code can be used to define a default value of s=100 wihtin the function? - ANSWERSif
nargin <4, s=100; end
The incremental search method uses input values spaced at ________ spaced intervals -
ANSWERSevenly
The bisection algorithm is an open method (T/F) - ANSWERSFalse
The bisection method is a bracketing method (T/F) - ANSWERSTrue
The main advantage of the secant method over the Newton-Raphson method is that the secant method
only requires analytically finding one derivative (T/F) - ANSWERSFalse
, What is the first step if you are asked to find all real roots of a function? - ANSWERSGraph the function
Which one of the followingfunctions can be used to find the number of roots of a function between a
specified lower and upper bound? - ANSWERSincsearch
The false position method is based on the false assumption that the function can be approximated y a(n)
___________. - ANSWERSstraight line
In the _________ method, the interval is divided in half and function is evaluated at the midpoint. -
ANSWERSBisection
In mathematics, a root of a function f(x) is a calue for x that products f(x) =0 (T/F) - ANSWERSTrue
The main advantage of the Newton-Raphson method is that it always converges (T/F) - ANSWERSFalse
Tangent points in a function can cause an opposite-valued bracket to contain an even number of roots.
(T/F) - ANSWERSTrue
A bracket with opposite-signed function values always contains exactly one root (T/F) - ANSWERSFalse
The main advantage of the secant method is that it as guaranteed to converge (T/F) - ANSWERSFalse
The secant method requires two initial estimates of x, but does not require an analytical expression of
the derivative (T/F) - ANSWERSTrue
Select the bracketing method(s) - ANSWERSFalse Position, Bisection.
Select the open method(s) - ANSWERSNewton-Raphson, Secant.
The main advantage of the modified secant method is that it does not require specifying a value for the
change in x. - ANSWERSFalse
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