Intro Analysis

Practice Questions

Introduction to Analysis › Intro Analysis

Page 1 of 4

10 of 33

Determine whether the following statement is true or false:

Some power series such as have a possible radius of convergence that can be found by computing the roots of the coefficients of .

Determine whether the following statement is true or false:

Let , , , and $d\ \epsilon\ \mathbb{R}$ . If and then .

What term does the following define.

A sequence of sets $\begin{Bmatrix} I_n \end{Bmatrix}_{n\ \epsilon\ \mathbb{N}}$ is __________ if and only if $I_1\supseteq I_2\supseteq ...$ .

Identify the following property.

For , , and $c\ \epsilon\ \mathbb{R}$ where and then this implies .

Determine whether the following statement is true or false:

Some power series such as have a possible radius of convergence that can be found by computing the roots of the coefficients of .

Determine whether the following statement is true or false:

If is a nonempty subset of $\mathbb{N}$ , then has a finite infimum and it is an element of .

What term has the following definition.

, $b\ \epsilon\ \mathbb{R}$ and . Over the interval is a set of points $P=\begin{Bmatrix} x_0,x_1,...,x_n \end{Bmatrix}$ such that

What term has the following definition.

, $b\ \epsilon\ \mathbb{R}$ and . Over the interval is a set of points $P=\begin{Bmatrix} x_0,x_1,...,x_n \end{Bmatrix}$ such that

What term does the following define.

A sequence of sets $\begin{Bmatrix} I_n \end{Bmatrix}_{n\ \epsilon\ \mathbb{N}}$ is __________ if and only if $I_1\supseteq I_2\supseteq ...$ .

Identify the following property.

For , , and $c\ \epsilon\ \mathbb{R}$ where and then this implies .

Page 1 of 4