Q.Let f(x) : [1,3] 3m R, m 21 be a mapping defined by -> if x is rational m +1 if x is irrational then the lower and upper Riemann sums equal to f(2) = { (a) /f(2)dx < f(x)d.x (b) / f(x)dx = / f(x)dx (c) /f(=)dr > f(x)dx (d) / f(x)dx and /f(x)dx do not exist. O a O b O c O d

Q.Let f(x) : [1,3] 3m R, m 21 be a mapping defined by -> if x is rational m +1 if x is irrational then the lower and upper Riemann sums equal to f(2) = { (a) /f(2)dx < f(x)d.x (b) / f(x)dx = / f(x)dx (c) /f(=)dr > f(x)dx (d) / f(x)dx and /f(x)dx do not exist. O a O b O c O d

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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Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

Q.Let f(x) : [1,3]
R, m 21 be a mapping defined by
->
if x is rational
m +1 if x is irrational
then the lower and upper Riemann sums equal to
3m
f(2) = {
(a) /r(2)dx < / f(2)da
(b) /
f(x)dx =
(c) / f(x)dx 2
(x)dx
(d) / f(x)dx and f(x)dx
do not
exist.
a
b

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