Let V=C(R) be the vector space of all continuous functions on our step the following sets w at subspaces of V ? justify your answera).w is the set of all differentiable functions.b) w is the set of all bounded continuous functions on R.c).w is the set of all non-negative valued functions on Rd). w is the set of all continuous functionse). w is the set of all polynomials with integer coefficients 2. a) Let V = C(R) be the vector space of all continuous functions on R. Which of the following setsW are subspaces of V? Justify your answer.i) W is the set of all differentiable functions on R.ii) W is the set of all bounded continuous functions on R.iii) W is the set of all non-negative-valued functions on R.iv) W is the set of all continuous odd functions.v) W is the set of all polynomials with integer co-efficients.

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Let V=C(R) be the vector space of all continuous functions on our step the following sets w at subspaces of V ? justify your answer a).w is the set of all differentiable functions. b) w is the set of all bounded continuous functions on R. c).w is the set of all non-negative valued functions on R

Let V=C(R) be the vector space of all continuous functions on our step the following sets w at subspaces of V ? justify your answer a).w is the set of all differentiable functions. b) w is the set of all bounded continuous functions on R. c).w is the set of all non-negative valued functions on R

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=C(R) be the vector space of all continuous functions on our step the following sets w at subspaces of V ? justify your answer

a).w is the set of all differentiable functions.

b) w is the set of all bounded continuous functions on R.

c).w is the set of all non-negative valued functions on R

d). w is the set of all continuous functions

e). w is the set of all polynomials with integer coefficients

2. a) Let V = C(R) be the vector space of all continuous functions on R. Which of the following sets
W are subspaces of V? Justify your answer.
i) W is the set of all differentiable functions on R.
ii) W is the set of all bounded continuous functions on R.
iii) W is the set of all non-negative-valued functions on R.
iv) W is the set of all continuous odd functions.
v) W is the set of all polynomials with integer co-efficients.

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

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