Correctly identify statements below as true or false about the integral test shown. * I an with f(n) = an n=1 and f(x)dx 1 true false f(x) must be continuous for x 21 the improper integral can converge and the series diverge series AND integral either вотH соnverge or Bотн diverge integral test give absolute convergence f(x) can have a lower bound of some x < 0 the lower bounds must match and sometimes requires some manipulation to achieve the lower bound must always be 1 f(x) must be decreasing so the series doesn't fail the nth term test the series has the same sum as what the improper integral

Correctly identify statements below as true or false about the integral test shown. * I an with f(n) = an n=1 and f(x)dx 1 true false f(x) must be continuous for x 21 the improper integral can converge and the series diverge series AND integral either вотH соnverge or Bотн diverge integral test give absolute convergence f(x) can have a lower bound of some x < 0 the lower bounds must match and sometimes requires some manipulation to achieve the lower bound must always be 1 f(x) must be decreasing so the series doesn't fail the nth term test the series has the same sum as what the improper integral

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

Series Condition 4

Correctly identify statements below as true or false about the integral test
shown. *
E an with f(n) = an
n = 1
and f(x)dx
true
false
f(x) must be continuous for x
21
the improper integral can
converge and the series
diverge
series AND integral either
BOTH converge or BOTH
diverge
integral test give absolute
convergence
f(x) can have a lower bound
of some x < 0
the lower bounds must
match and sometimes
requires some manipulation
to achieve
the lower bound must always
be 1
f(x) must be decreasing so
the series doesn't fail the nth
term test
the series has the same sum
as what the improper integral
converges to
terms must be positive

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