Nonlinear Equations Your nonlinearity confuses me

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Nonlinear EquationsYour nonlinearity
confuses me
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The problem of not knowing what we missed is
that we believe we haven't missed anything
Stephen Chew on Multitasking
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Example General Engineering

• You are working for DOWN THE TOILET COMPANY
  that makes floats for ABC commodes. The floating
  ball has a specific gravity of 0.6 and has a
  radius of 5.5 cm. You are asked to find the
  depth to which the ball is submerged when
  floating in water.

Figure Diagram of the floating ball
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For the trunnion-hub problem discussed on first
day of class where we were seeking contraction of
0.015, did the trunnion shrink enough when
dipped in dry-ice/alcohol mixture?

1. Yes
2. No

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Example Mechanical Engineering
Since the answer was a resounding NO, a logical
question to ask would be If the temperature
of -108oF is not enough for the contraction,
what is?
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Finding The Temperature of the Fluid
Ta 80oF Tc ???oF D 12.363" ?D -0.015"
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Finding The Temperature of the Fluid
Ta 80oF Tc ???oF D 12.363" ?D -0.015"
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Nonlinear Equations(Background)
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How many roots can a nonlinear equation have?
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How many roots can a nonlinear equation have?
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How many roots can a nonlinear equation have?
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How many roots can a nonlinear equation have?
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The value of x that satisfies f (x)0 is called
the

1. root of equation f (x)0
2. root of function f (x)
3. zero of equation f (x)0
4. none of the above

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A quadratic equation has ______ root(s)

1. one
2. two
3. three
4. cannot be determined

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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

1. one
2. two
3. three
4. cannot be determined

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

1. zero
2. one
3. two
4. infinite

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A polynomial of order n has zeros

1. n -1
2. n
3. n 1
4. n 2

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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 ___.

1. 0.1823 s
2. 0.3979 s
3. 0.9162 s
4. 1.609 s

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END
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Newton Raphson Method
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Newton-Raphson method of finding roots of
nonlinear equations falls under the category of
__________ method.

1. bracketing
2. open
3. random
4. graphical

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The next iterative value of the root of the
equation x 24 using Newton-Raphson method, if
the initial guess is 3 is

1. 1.500
2. 2.066
3. 2.166
4. 3.000

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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

1. -3.2470
2. -0.2470
3. 3.2470
4. 6.2470

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

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END
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Bisection Method
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Bisection method of finding roots of nonlinear
equations falls under the category of a (an)
method.

1. open
2. bracketing
3. random
4. 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)

1. one root
2. undeterminable number of roots
3. no root
4. at least one root

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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

1. f (t) 5e-t40
2. f (t) 5e-t46
3. f (t) 5e-t2
4. f (t) 5e-t-20

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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

1. 0 Et2.5
2. 0 Et 5
3. 0 Et 10
4. 0 Et 20

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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)x 2

1. is a polynomial
2. has repeated zeros at x0
3. is always non-negative
4. slope is zero at x0

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ENDhttp//numericalmethods.eng.usf.eduNumer
ical Methods for the STEM undergraduate
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How and Why?
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Study Groups Help?
Studying Alone
Studying with Peers
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END
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Final Grade vs. First Test Grade
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