- 3.6.1: Show that if (x,.) is an unbounded sequence, then there exists a pr...
- 3.6.2: Give examples of properly divergent sequences (x,.) and (y,.) withY...
- 3.6.3: Show that if x,. > 0 for all n eN, then lim(x,.) = 0 if and only if...
- 3.6.4: Establish the proper divergence of the following sequences. (a) ( J...
- 3.6.5: Is the sequence (n sin n) properly divergent?
- 3.6.6: Let (x,.) be properly divergent and let (y,.) be such that lim(x,.y...
- 3.6.7: Let (x,.) and (y,.) be sequences of positive numbers such that lim(...
- 3.6.8: Investigate the convergence or the divergence of the following sequ...
- 3.6.9: Let (x,.) and (y,.) be sequences of positive numbers such that lim(...
- 3.6.10: Show that if lim(a,./n) = L, where L > 0, then lim(a,.) = +oo.
Solutions for Chapter 3.6: Properly Divergent Sequences
Full solutions for Introduction to Real Analysis | 3rd Edition
Addition principle of probability.
P(A or B) = P(A) + P(B) - P(A and B). If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)
Angle between vectors
The angle formed by two nonzero vectors sharing a common initial point
An angle whose vertex is the center of a circle
A letter or symbol that stands for a specific number,
Convergence of a series
A series aqk=1 ak converges to a sum S if imn: q ank=1ak = S
Unit of measurement (represented by the symbol ) for angles or arcs, equal to 1/360 of a complete revolution
Difference of complex numbers
(a + bi) - (c + di) = (a - c) + (b - d)i
equation of a quadratic function
ƒ(x) = ax 2 + bx + c(a ? 0)
The left side of u(v + w) = uv + uw.
See Mathematical induction.
The instantaneous rate of change of a position function with respect to time, p. 737.
Law of cosines
a2 = b2 + c2 - 2bc cos A, b2 = a2 + c2 - 2ac cos B, c2 = a2 + b2 - 2ab cos C
Linear regression equation
Equation of a linear regression line
A system of linear equations
Multiplicative inverse of a matrix
See Inverse of a matrix
Data items more than 1.5 times the IQR below the first quartile or above the third quartile.
Any number that can be written as a decimal.
Reflection through the origin
x, y and (-x,-y) are reflections of each other through the origin.
Sum of complex numbers
(a + bi) + (c + di) = (a + c) + (b + d)i
x = a.
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