Register

Homework Help Question and Answers

Submit a new Query

Recent Homework Help Question & Answers


Question 43427

posted 11 months ago

5. Let X,Y, Z be nonempty subsets of Euclidean spaces. [Each part is worth 10pt]

View answer

Question 43425

posted 11 months ago

Let X be a non-empty set. [Each part is worth 5pt]
\text { (a) Let } d: X \times X \rightarrow \mathbf{R}_{+} \text {be defined as }
d(x, y)=\left\{\begin{array}{ll} 0 & \text { if } x=y \\ 1 & \text { if } x \neq y \end{array}\right.
Show that d is a metric on X. This metric is called discrete.
(b) Let d be a metric on X and let f : R4 → R4. If ƒ is strictly increasing, is it true that fod is a metric on X?

View answer

Question 43428

posted 11 months ago

Q6. Let (X, d) and (Y, p) be metric spaces. Show that the following two definitions of lower hemicontinuity are equivalent. [Each direction is worth 10pt]

View answer

Question 43426

posted 11 months ago

Prove the following statements. [Each part is worth 5pt
(a) Let {rn} be a converging sequence in a metric space X and let x € X be its limit. Use the definition of compactness to show that the set {x}U{xn} is compact.
(b) Show that a subset of a metric space X is closed if and only if its intersection with every compact subset of X is closed.

View answer

Question 37438

posted 1 years ago

If the Taylor series for f(x) = e²+1 about x = 0 is truncated after the 10th term and is then used to compute e³, what bound on the error can be given?

View answer

Question 37439

posted 1 years ago

- The hypothetical computer, Shelly-32 has word lengths of 32 bits (32 binary digits).

View answer

Question 29739

posted 1 years ago

\text { 3. If } s_{1}=\sqrt{\frac{n}{2}}^{n \rightarrow \infty} \text { and }
s_{n+1}=\sqrt{2+\sqrt{s_{n}}} \quad(n=1,2,3, \ldots)
prove that {s.} converges, and that s. <2 for n=1, 2, 3, ....%3D

View answer

Question 29740

posted 1 years ago

In problem number 2, once you compute the limit, show that the sequence converges to that limit using the definition.

View answer

Question 29738

posted 1 years ago

\text { 2. Calculate } \lim \left(\sqrt{n^{2}+n}-n\right) \text {. }

View answer

Question 29741

posted 1 years ago

Prove that a sequence {pn} converges to p if and only if every subsequence of {pn}converges to p. Hint: For one of the implications, consider the subsequences with only even indices {p2n} and the one with only odd indices {p2n+1}.

View answer

Questions not Found

Most popular subject

Thermodynamics

Essay/Summary

Mechanics

Complex Analysis

Engineering Economics

Calculus

Modern Physics

General Chemistry

Strength Of Materials

Fluid Mechanics

x