If $lim_{xto c^-}${$ln x$} and $lim_{xto c^+}${$ln x$} exists finitely but they are not equal
$begingroup$
If $lim_{xto c^-}${$ln x$} and $lim_{xto c^+}${$ln x$} exists finitely but they are not equal (where {} denotes fractional part function),then
$(a)c$ can take only rational values
$(b)c$ can take only irrational values
$(c)c$ can take infinite values in which only one is irrational
$(d)c$ can take infinite values in which only one is rational
I do not know how to start attempting this question.Its answer given is option $(d)$ Graphing calculator is not allowed.
limits fractional-part
asked Dec 27 '18 at 15:13
user984325user984325
246112
$endgroup$
add a comment |
$begingroup$
If $lim_{xto c^-}${$ln x$} and $lim_{xto c^+}${$ln x$} exists finitely but they are not equal (where {} denotes fractional part function),then
$(a)c$ can take only rational values
$(b)c$ can take only irrational values
$(c)c$ can take infinite values in which only one is irrational
$(d)c$ can take infinite values in which only one is rational
I do not know how to start attempting this question.Its answer given is option $(d)$ Graphing calculator is not allowed.
limits fractional-part
asked Dec 27 '18 at 15:13
user984325user984325
246112
$endgroup$
add a comment |
$begingroup$
If $lim_{xto c^-}${$ln x$} and $lim_{xto c^+}${$ln x$} exists finitely but they are not equal (where {} denotes fractional part function),then
$(a)c$ can take only rational values
$(b)c$ can take only irrational values
$(c)c$ can take infinite values in which only one is irrational
$(d)c$ can take infinite values in which only one is rational
I do not know how to start attempting this question.Its answer given is option $(d)$ Graphing calculator is not allowed.
limits fractional-part
asked Dec 27 '18 at 15:13
user984325user984325
246112
$endgroup$
If $lim_{xto c^-}${$ln x$} and $lim_{xto c^+}${$ln x$} exists finitely but they are not equal (where {} denotes fractional part function),then
$(a)c$ can take only rational values
$(b)c$ can take only irrational values
$(c)c$ can take infinite values in which only one is irrational
$(d)c$ can take infinite values in which only one is rational
I do not know how to start attempting this question.Its answer given is option $(d)$ Graphing calculator is not allowed.
limits fractional-part
limits fractional-part
asked Dec 27 '18 at 15:13
user984325user984325
246112
asked Dec 27 '18 at 15:13
user984325user984325
246112
asked Dec 27 '18 at 15:13
user984325user984325
246112
asked Dec 27 '18 at 15:13
user984325user984325
246112
asked Dec 27 '18 at 15:13
user984325user984325
246112
246112
add a comment |
add a comment |
1 Answer
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$begingroup$
Hint: The only way that the limits cannot be equal is if $ln c$ is an integer.
Bigger hint: Hover over the greyed out box to reveal.
$ln c$ is an integer if and only if $c = e^n$ for some integer $n$, and the only integer $n$ for which $e^n$ is rational is $n=0$.
answered Dec 27 '18 at 15:19
Clive NewsteadClive Newstead
51.7k474135
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1 Answer
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1 Answer
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$begingroup$
Hint: The only way that the limits cannot be equal is if $ln c$ is an integer.
Bigger hint: Hover over the greyed out box to reveal.
$ln c$ is an integer if and only if $c = e^n$ for some integer $n$, and the only integer $n$ for which $e^n$ is rational is $n=0$.
answered Dec 27 '18 at 15:19
Clive NewsteadClive Newstead
51.7k474135
$endgroup$
add a comment |
$begingroup$
Hint: The only way that the limits cannot be equal is if $ln c$ is an integer.
Bigger hint: Hover over the greyed out box to reveal.
$ln c$ is an integer if and only if $c = e^n$ for some integer $n$, and the only integer $n$ for which $e^n$ is rational is $n=0$.
answered Dec 27 '18 at 15:19
Clive NewsteadClive Newstead
51.7k474135
$endgroup$
add a comment |
$begingroup$
Hint: The only way that the limits cannot be equal is if $ln c$ is an integer.
Bigger hint: Hover over the greyed out box to reveal.
$ln c$ is an integer if and only if $c = e^n$ for some integer $n$, and the only integer $n$ for which $e^n$ is rational is $n=0$.
answered Dec 27 '18 at 15:19
Clive NewsteadClive Newstead
51.7k474135
$endgroup$
Hint: The only way that the limits cannot be equal is if $ln c$ is an integer.
Bigger hint: Hover over the greyed out box to reveal.
$ln c$ is an integer if and only if $c = e^n$ for some integer $n$, and the only integer $n$ for which $e^n$ is rational is $n=0$.
answered Dec 27 '18 at 15:19
Clive NewsteadClive Newstead
51.7k474135
answered Dec 27 '18 at 15:19
Clive NewsteadClive Newstead
51.7k474135
answered Dec 27 '18 at 15:19
Clive NewsteadClive Newstead
51.7k474135
answered Dec 27 '18 at 15:19
Clive NewsteadClive Newstead
51.7k474135
51.7k474135
add a comment |
add a comment |
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