Exam 14: Numerical Methods

Typically, ____ equations involve trigonometric, exponential, or logarithmic functions and cannot be reduced to any polynomial equation in x .

Of the three bisection methods, the ___________________ is probably the most efficient for common problems.

Determining the optimum ____________________ (slope-reduction) factor is almost always an extremely difficult problem in any calculation.

The art of ____________________ analysis consists in balancing time spent optimizing a problem s solution before computation against time spent correcting unforeseen errors during computation.

Irrational numbers and transcendental numbers are represented by ____________________ decimal fractions and cannot be expressed as simple fractions.

In the ordinary ____________________ method, the only feature of the function that is monitored is its sign.

The area under a curve can be approximated by connecting a line between two points on the curve and calculating the area under that line. The shape created is called a(n) ____________________.

A drawback of the ____________________ method is that even though the method converges more rapidly to a value of x that results in a small |f(x)| , the interval containing the root does not diminish significantly.

The ____ of a function of a single variable can be thought of as the area under a curve.

Simpson s rule is a popular method of evaluating integrals of functions that are smooth.