Let V and W be normed vector spaces and let f : V → W be diﬀerentiable at a ∈ V . Let h ∈ V . In each case decide whether the statement is always true: a Df(a)(h) is a linear map from V to W b Df(a) ∈ W c Df(a)(h) ∈ W d Df is a continuous map from V to W.

Let V and W be normed vector spaces and let f : V → W be diﬀerentiable at a ∈ V . Let h ∈ V . In each case decide whether the statement is always true: a Df(a)(h) is a linear map from V to W b Df(a) ∈ W c Df(a)(h) ∈ W d Df is a continuous map from V to W.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let V and W be normed vector spaces and let f : V → W be diﬀerentiable at a ∈ V . Let h ∈ V . In each case decide whether the statement is always true:
a Df(a)(h) is a linear map from V to W
b Df(a) ∈ W
c Df(a)(h) ∈ W
d Df is a continuous map from V to W.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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