Numerical Methods Exam 1-Answered
In solving an engineering problem, the sequence of the four major steps is:
a. model, validate, formulate, solve
b. model, solve, formulate, validate
c. formulate, model, solve, validate
d. model, formulate, solve, validate - ANS-d. model, formulate, solve, validate
A root of a smooth transcendental function f(x) is
a. the value of x where the function f(x) crosses the x-axis
b. the value of x where the function f(x) evaluates to zero
c. all of the choices shown
d. the value of x where the function f(x) evaluates to x - ANS-b. the value of x
where the function f(x) evaluates to zero
Given a smooth transcendental function f(x), if f(a) * f(b) is less than zero then the
open x-interval (a, b)
a. all of the choices shown are possible
b. contains an odd number of roots of function f(x)
c. contains no root of f(x)
d. contains an even number of roots of the function f(x) - ANS-b. contains an odd
number of roots of function f(x)
Given a smooth transcendental function f(x), if f(a) * f(b) is greater than zero then
the open x-interval (a, b)
a. all of the choices shown are possible
b. contains no root of f(x)
c. contains two unique roots of the function f(x)
d. contains an even number of roots of the function f(x) - ANS-a. all of the choices
shown are possible
A quadratic algebraic function: f(x) = a * x2 + b * x + c
a. may have two unique real roots
b. may have two equal real roots
c. all of the choices shown are possible
d. may have two complex roots that are complex conjugates - ANS-c. all of the
choices shown are possible
The quadratic equation: 2x2 - 3x + 5 = 0 has
a. none of the choices shown
b. no real roots
c. two equal real roots
d. two unique real roots - ANS-b. no real roots
The quadratic equation: 2x2 - 3x - 5 = 0 has
, a. two equal real roots
b. no real roots
c. two unique real roots
d. none of the choices shown - ANS-c. two unique real roots
The quadratic equation: 2x2 + 20x + 50 = 0 has
a. two equal real roots
b. none of the choices shown
c. no real roots
d. two unique real roots - ANS-a. two equal real roots
The function f(x) = 2 * e-x - sin(x) has a root {please note that x is in radians}
a. x = 3.5 ± 0.2
b. x = 1 ± 0.2
c. x = -1 ± 0.2
d. all of the choices shown - ANS-b. x = 1 ± 0.2
The function f(x) = ex - 3x2 has a root
a. 3.20 ± 0.02
b. 0.50 ± 0.02
c. 0.90 ± 0.02
d. 2.65 ± 0.02 - ANS-c. 0.90 ± 0.02
The Bisection Method for finding root of a transcendental function f(x) belongs to
the following category:
a. Random
b. Open or Non-bracketing
c. Graphical
d. Bracketing - ANS-d. Bracketing
In finding root of a transcendental function f(x) by the Bisection method, if the
absolute error bound is 0.0004 then the approximate root value has
a. at least four correct decimal digits
b. at least three significant digits
c. at least four significant digits
d. at least three correct decimal digits - ANS-d. at least three correct decimal digits
In finding root of a transcendental function f(x) by the Bisection method, if the
relative error bound is 0.0004 then the approximate root value has
a. at least three correct decimal digits
b. at least three significant digits
c. at least four significant digits
d. at least four correct decimal digits - ANS-b. at least three significant digits
In finding root of a transcendental function f(x) by the Bisection method, if the
relative error bound is 0.00006 then the approximate root value has
a. at least four significant digits
b. at least three correct decimal digits
In solving an engineering problem, the sequence of the four major steps is:
a. model, validate, formulate, solve
b. model, solve, formulate, validate
c. formulate, model, solve, validate
d. model, formulate, solve, validate - ANS-d. model, formulate, solve, validate
A root of a smooth transcendental function f(x) is
a. the value of x where the function f(x) crosses the x-axis
b. the value of x where the function f(x) evaluates to zero
c. all of the choices shown
d. the value of x where the function f(x) evaluates to x - ANS-b. the value of x
where the function f(x) evaluates to zero
Given a smooth transcendental function f(x), if f(a) * f(b) is less than zero then the
open x-interval (a, b)
a. all of the choices shown are possible
b. contains an odd number of roots of function f(x)
c. contains no root of f(x)
d. contains an even number of roots of the function f(x) - ANS-b. contains an odd
number of roots of function f(x)
Given a smooth transcendental function f(x), if f(a) * f(b) is greater than zero then
the open x-interval (a, b)
a. all of the choices shown are possible
b. contains no root of f(x)
c. contains two unique roots of the function f(x)
d. contains an even number of roots of the function f(x) - ANS-a. all of the choices
shown are possible
A quadratic algebraic function: f(x) = a * x2 + b * x + c
a. may have two unique real roots
b. may have two equal real roots
c. all of the choices shown are possible
d. may have two complex roots that are complex conjugates - ANS-c. all of the
choices shown are possible
The quadratic equation: 2x2 - 3x + 5 = 0 has
a. none of the choices shown
b. no real roots
c. two equal real roots
d. two unique real roots - ANS-b. no real roots
The quadratic equation: 2x2 - 3x - 5 = 0 has
, a. two equal real roots
b. no real roots
c. two unique real roots
d. none of the choices shown - ANS-c. two unique real roots
The quadratic equation: 2x2 + 20x + 50 = 0 has
a. two equal real roots
b. none of the choices shown
c. no real roots
d. two unique real roots - ANS-a. two equal real roots
The function f(x) = 2 * e-x - sin(x) has a root {please note that x is in radians}
a. x = 3.5 ± 0.2
b. x = 1 ± 0.2
c. x = -1 ± 0.2
d. all of the choices shown - ANS-b. x = 1 ± 0.2
The function f(x) = ex - 3x2 has a root
a. 3.20 ± 0.02
b. 0.50 ± 0.02
c. 0.90 ± 0.02
d. 2.65 ± 0.02 - ANS-c. 0.90 ± 0.02
The Bisection Method for finding root of a transcendental function f(x) belongs to
the following category:
a. Random
b. Open or Non-bracketing
c. Graphical
d. Bracketing - ANS-d. Bracketing
In finding root of a transcendental function f(x) by the Bisection method, if the
absolute error bound is 0.0004 then the approximate root value has
a. at least four correct decimal digits
b. at least three significant digits
c. at least four significant digits
d. at least three correct decimal digits - ANS-d. at least three correct decimal digits
In finding root of a transcendental function f(x) by the Bisection method, if the
relative error bound is 0.0004 then the approximate root value has
a. at least three correct decimal digits
b. at least three significant digits
c. at least four significant digits
d. at least four correct decimal digits - ANS-b. at least three significant digits
In finding root of a transcendental function f(x) by the Bisection method, if the
relative error bound is 0.00006 then the approximate root value has
a. at least four significant digits
b. at least three correct decimal digits
