Lets $h:[a,b] rightarrow R$, $f:[a,b]rightarrow R$ increasing and $t_1,t_2,…,t_n$ $in [a,b]$. [on hold]Prove that a set $T_1$is finite iff there is a bijection from it onto a finite set $T_2$An inequality for some seriesProve that $(k_n)$ and $(t_n)$ converge to the same limit.Check proof that, if $0 < k_1 < t_1$, $k_n+1= sqrtk_nt_n$ and $t_n+1=(k_n+t_n)/2$, then $0leq t_n+1- k_n+1 leq (t_1-k_1)/2^n$Proof Verification: Prove if $s_n rightarrow -1$ and $t_n rightarrow 3$, then $s_n(t_n-1) rightarrow -2$Show that the sequence is increasing and unboundedShow that the barycentric coordinates $t_o(x), t_1(x),…,t_n(x)$ continually depend on $x$.If $I$ an interval and $x_1,x_2,x_3in I$, why $t_1x_1+t_2x_2+t_3x_3in I$ when $t_1+t_2+t_3=1, t_iin [0,1]$?Prove that a nonempty set $T_1$ is finite if and only if there is a bijection from $T_1$ onto a finite set $T_2.$Lets $g_1$ and $g_2$ Riemann integrable functions in $[a,b]$ such that ..
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Lets $h:[a,b] rightarrow R$, $f:[a,b]rightarrow R$ increasing and $t_1,t_2,…,t_n$ $in [a,b]$. [on hold]
Prove that a set $T_1$is finite iff there is a bijection from it onto a finite set $T_2$An inequality for some seriesProve that $(k_n)$ and $(t_n)$ converge to the same limit.Check proof that, if $0 < k_1 < t_1$, $k_n+1= sqrtk_nt_n$ and $t_n+1=(k_n+t_n)/2$, then $0leq t_n+1- k_n+1 leq (t_1-k_1)/2^n$Proof Verification: Prove if $s_n rightarrow -1$ and $t_n rightarrow 3$, then $s_n(t_n-1) rightarrow -2$Show that the sequence is increasing and unboundedShow that the barycentric coordinates $t_o(x), t_1(x),…,t_n(x)$ continually depend on $x$.If $I$ an interval and $x_1,x_2,x_3in I$, why $t_1x_1+t_2x_2+t_3x_3in I$ when $t_1+t_2+t_3=1, t_iin [0,1]$?Prove that a nonempty set $T_1$ is finite if and only if there is a bijection from $T_1$ onto a finite set $T_2.$Lets $g_1$ and $g_2$ Riemann integrable functions in $[a,b]$ such that ..
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Lets $h:[a,b] rightarrow R$, $f:[a,b]rightarrow R$ increasing and $t_1,t_2,...,t_n$ $in [a,b]$. Prove that if $sum_i=1^nh(t_i) geq 0$ and $f(a)geq 0$, then $f(a) sum_i=1^nh(t_i) leq sum_i=1^nf(t_i)h(t_i)$.
real-analysis
asked Mar 10 at 19:36
Mayra FerreiraMayra Ferreira
1
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put on hold as off-topic by RRL, Math1000, Alex Provost, Eevee Trainer, Carl Mummert 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – RRL, Math1000, Alex Provost, Eevee Trainer, Carl Mummert
add a comment |
$begingroup$
Lets $h:[a,b] rightarrow R$, $f:[a,b]rightarrow R$ increasing and $t_1,t_2,...,t_n$ $in [a,b]$. Prove that if $sum_i=1^nh(t_i) geq 0$ and $f(a)geq 0$, then $f(a) sum_i=1^nh(t_i) leq sum_i=1^nf(t_i)h(t_i)$.
real-analysis
asked Mar 10 at 19:36
Mayra FerreiraMayra Ferreira
1
New contributor
Mayra Ferreira is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
put on hold as off-topic by RRL, Math1000, Alex Provost, Eevee Trainer, Carl Mummert 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – RRL, Math1000, Alex Provost, Eevee Trainer, Carl Mummert
$begingroup$
Hi and welcome to the Math.SE. "Do it for me" questions are customarily poorly received by other members so, in order to get an answer, it is better to avoid asking them. You should show your commitment in solving the problem: what did you tried? Where did you failed? Show them that you really need a helping because you want to learn.
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– Daniele Tampieri
Mar 10 at 19:45
add a comment |
$begingroup$
Lets $h:[a,b] rightarrow R$, $f:[a,b]rightarrow R$ increasing and $t_1,t_2,...,t_n$ $in [a,b]$. Prove that if $sum_i=1^nh(t_i) geq 0$ and $f(a)geq 0$, then $f(a) sum_i=1^nh(t_i) leq sum_i=1^nf(t_i)h(t_i)$.
real-analysis
asked Mar 10 at 19:36
Mayra FerreiraMayra Ferreira
1
New contributor
Mayra Ferreira is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Lets $h:[a,b] rightarrow R$, $f:[a,b]rightarrow R$ increasing and $t_1,t_2,...,t_n$ $in [a,b]$. Prove that if $sum_i=1^nh(t_i) geq 0$ and $f(a)geq 0$, then $f(a) sum_i=1^nh(t_i) leq sum_i=1^nf(t_i)h(t_i)$.
real-analysis
real-analysis
asked Mar 10 at 19:36
Mayra FerreiraMayra Ferreira
1
New contributor
Mayra Ferreira is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Mar 10 at 19:36
Mayra FerreiraMayra Ferreira
1
New contributor
Mayra Ferreira is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Mar 10 at 19:36
Mayra FerreiraMayra Ferreira
1
New contributor
Mayra Ferreira is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Mar 10 at 19:36
Mayra FerreiraMayra Ferreira
1
asked Mar 10 at 19:36
Mayra FerreiraMayra Ferreira
1
1
New contributor
Mayra Ferreira is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Mayra Ferreira is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Mayra Ferreira is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by RRL, Math1000, Alex Provost, Eevee Trainer, Carl Mummert 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – RRL, Math1000, Alex Provost, Eevee Trainer, Carl Mummert
put on hold as off-topic by RRL, Math1000, Alex Provost, Eevee Trainer, Carl Mummert 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – RRL, Math1000, Alex Provost, Eevee Trainer, Carl Mummert
$begingroup$
Hi and welcome to the Math.SE. "Do it for me" questions are customarily poorly received by other members so, in order to get an answer, it is better to avoid asking them. You should show your commitment in solving the problem: what did you tried? Where did you failed? Show them that you really need a helping because you want to learn.
$endgroup$
– Daniele Tampieri
Mar 10 at 19:45
add a comment |
$begingroup$
Hi and welcome to the Math.SE. "Do it for me" questions are customarily poorly received by other members so, in order to get an answer, it is better to avoid asking them. You should show your commitment in solving the problem: what did you tried? Where did you failed? Show them that you really need a helping because you want to learn.
$endgroup$
– Daniele Tampieri
Mar 10 at 19:45
$begingroup$
Hi and welcome to the Math.SE. "Do it for me" questions are customarily poorly received by other members so, in order to get an answer, it is better to avoid asking them. You should show your commitment in solving the problem: what did you tried? Where did you failed? Show them that you really need a helping because you want to learn.
$endgroup$
– Daniele Tampieri
Mar 10 at 19:45
$begingroup$
Hi and welcome to the Math.SE. "Do it for me" questions are customarily poorly received by other members so, in order to get an answer, it is better to avoid asking them. You should show your commitment in solving the problem: what did you tried? Where did you failed? Show them that you really need a helping because you want to learn.
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– Daniele Tampieri
Mar 10 at 19:45
add a comment |
1 Answer
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Your statement is not true. Consider the interval $[a,b] = [0,2]$ and $f : [0,2] rightarrow mathbbR$ defined by $f(x)=x$ (so $f$ is increasing), and $h : [0,2] rightarrow mathbbR$ defined by $h(x)=3-2x$. Consider $t_1 = 1$ and $t_2 = 2$.
You have $f(a)(h(t_1)+h(t_2))=0$ but $f(t_1)h(t_1)+f(t_2)h(t_2) = -1$.
answered Mar 10 at 21:18
TheSilverDoeTheSilverDoe
3,837112
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add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Your statement is not true. Consider the interval $[a,b] = [0,2]$ and $f : [0,2] rightarrow mathbbR$ defined by $f(x)=x$ (so $f$ is increasing), and $h : [0,2] rightarrow mathbbR$ defined by $h(x)=3-2x$. Consider $t_1 = 1$ and $t_2 = 2$.
You have $f(a)(h(t_1)+h(t_2))=0$ but $f(t_1)h(t_1)+f(t_2)h(t_2) = -1$.
answered Mar 10 at 21:18
TheSilverDoeTheSilverDoe
3,837112
$endgroup$
add a comment |
$begingroup$
Your statement is not true. Consider the interval $[a,b] = [0,2]$ and $f : [0,2] rightarrow mathbbR$ defined by $f(x)=x$ (so $f$ is increasing), and $h : [0,2] rightarrow mathbbR$ defined by $h(x)=3-2x$. Consider $t_1 = 1$ and $t_2 = 2$.
You have $f(a)(h(t_1)+h(t_2))=0$ but $f(t_1)h(t_1)+f(t_2)h(t_2) = -1$.
answered Mar 10 at 21:18
TheSilverDoeTheSilverDoe
3,837112
$endgroup$
add a comment |
$begingroup$
Your statement is not true. Consider the interval $[a,b] = [0,2]$ and $f : [0,2] rightarrow mathbbR$ defined by $f(x)=x$ (so $f$ is increasing), and $h : [0,2] rightarrow mathbbR$ defined by $h(x)=3-2x$. Consider $t_1 = 1$ and $t_2 = 2$.
You have $f(a)(h(t_1)+h(t_2))=0$ but $f(t_1)h(t_1)+f(t_2)h(t_2) = -1$.
answered Mar 10 at 21:18
TheSilverDoeTheSilverDoe
3,837112
$endgroup$
Your statement is not true. Consider the interval $[a,b] = [0,2]$ and $f : [0,2] rightarrow mathbbR$ defined by $f(x)=x$ (so $f$ is increasing), and $h : [0,2] rightarrow mathbbR$ defined by $h(x)=3-2x$. Consider $t_1 = 1$ and $t_2 = 2$.
You have $f(a)(h(t_1)+h(t_2))=0$ but $f(t_1)h(t_1)+f(t_2)h(t_2) = -1$.
answered Mar 10 at 21:18
TheSilverDoeTheSilverDoe
3,837112
answered Mar 10 at 21:18
TheSilverDoeTheSilverDoe
3,837112
answered Mar 10 at 21:18
TheSilverDoeTheSilverDoe
3,837112
answered Mar 10 at 21:18
TheSilverDoeTheSilverDoe
3,837112
3,837112
add a comment |
add a comment |
$begingroup$
Hi and welcome to the Math.SE. "Do it for me" questions are customarily poorly received by other members so, in order to get an answer, it is better to avoid asking them. You should show your commitment in solving the problem: what did you tried? Where did you failed? Show them that you really need a helping because you want to learn.
$endgroup$
– Daniele Tampieri
Mar 10 at 19:45