Nonlinear Equations Clicker Quiz http:numericalmethods'eng'usf'edu Numerical Methods for the STEM un

1
Nonlinear Equations(Clicker Quiz)http//numer
icalmethods.eng.usf.eduNumerical Methods for the
STEM undergraduate
2
Nonlinear Equations(Background)http//numeric
almethods.eng.usf.eduNumerical Methods for the
STEM undergraduate
3
The value of x that satisfies f (x)0 is called
the

• root of equation f (x)0
• root of function f (x)
• zero of equation f (x)0
• none of the above

4
A quadratic equation has ______ root(s)

• one
• two
• three
• cannot be determined

5
For a certain cubic equation, at least one of the
roots is known to be a complex root. The total
number of complex roots the cubic equation has is

• one
• two
• three
• cannot be determined

6
Equation such as tan (x)x has __ root(s)

• zero
• one
• two
• infinite

7
A polynomial of order n has zeros

• n -1
• n
• n 1
• n 2

8
The velocity of a body is given by v (t)5e-t4,
where t is in seconds and v is in m/s. The
velocity of the body is 6 m/s at t

• 0.1823 s
• 0.3979 s
• 0.9162 s
• 1.609 s

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Bisection Method http//numericalmethods.eng.u
sf.eduNumerical Methods for the STEM
undergraduate
10
Bisection method of finding roots of nonlinear
equations falls under the category of a (an)
method.

• open
• bracketing
• random
• graphical

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If for a real continuous function f(x),f (a) f
(b)lt0, then in the range a,b for f(x)0, there
is (are)

• one root
• undeterminable number of roots
• no root
• at least one root

12
For an equation like x20, a root exists at x0.
The bisection method cannot be adopted to solve
this equation in spite of the root existing at
x0 because the function f(x)x2

• is a polynomial
• has repeated roots at x0
• is always non-negative
• slope is zero at x0

13
The velocity of a body is given by v(t)5e-t4,
where t is in seconds and v is in m/s. We want
to find the time when the velocity of the body is
6 m/s. The equation form needed for bisection
and Newton-Raphson methods is

• f(t) 5e-t40
• f(t) 5e-t46
• f(t) 5e-t2
• f(t) 5e-t-20

14
To find the root of an equation f(x)0, a student
started using the bisection method with a valid
bracket of 20,40. The smallest range for the
absolute true error at the end of the 2nd
iteration is

• 0 Et2.5
• 0 Et 5
• 0 Et 10
• 0 Et 20

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Newton Raphson Methodhttp//numericalmethods.e
ng.usf.eduNumerical Methods for the STEM
undergraduate
16
Newton-Raphson method of finding roots of
nonlinear equations falls under the category of
__________ method.

• bracketing
• open
• random
• graphical

17
The Newton-Raphson method formula for finding the
square root of a real number R from the equation
x2-R0 is,

• (A)
• (B)
• (C)
• (D)

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The next iterative value of the root of the
equation x2-4 using Newton-Raphson method, if the
initial guess is 3 is

• 1.5
• 2.066
• 2.166
• 3.00

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The root of equation f(x)0 is found by using
Newton-Raphson method. The initial estimate of
the root is xo3, f(3)5. The angle the tangent
to the function f(x) makes at x3 is 57o. The
next estimate of the root, x1 most nearly is

• -3.2470
• -0.2470
• 3.2470
• 6.2470