SOLUTION: A) what do you mean by a rational number? Give an example of a rational number and an irrational number.
B) rewrite 0.32727272727 as a rational number.
C) Give an example of
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Question 310822: A) what do you mean by a rational number? Give an example of a rational number and an irrational number.
B) rewrite 0.32727272727 as a rational number.
C) Give an example of a rational function and a polynomial function.
D) differentiate a hole and an essential discontinuity of a function.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
A rational number is a number that can be expressed as the ratio of two integers. An irrational number cannot be so expressed.
is a rational number
is a rational number
is an irrational number. It is also an algebraic number (it is the root of a non-constant polynomial equation with rational coefficients).
is a transcendental irrational number (it is irrational AND it is NOT the root of any non-constant polynomial equation with rational coefficients)
\ =\ \frac{2x\ +\ 1}{(x\ +\ 2)^3})
is a rational function.
\ =\ \alpha_0x^n\ +\ \alpha_1x^{n-1}\ +\ \alpha_3x^{n-2}\ +\ \cdots\ +\ \alpha_{n-2}x^2\ +\ \alpha_{n-1}x\ +\ \alpha_n)
is an 
degree polynomial equation if 
A hole is a hole in a graph. That is, a discontinuity that can be "repaired" by filling in a single point. In other words, a removable discontinuity is a point at which a graph is not connected but can be made connected by filling in a single point.
Formally, a removable discontinuity is one at which the limit of the function exists but does not equal the value of the function at that point; this may be because the function does not exist at that point.
Essential Discontinuity
Any discontinuity that is not removable. That is, a place where a graph is not connected and cannot be made connected simply by filling in a single point. Step discontinuities and vertical asymptotes are two types of essential discontinuities.
Formally, an essential discontinuity is a discontinuity at which the limit of the function does not exist.
John
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