Evaluate the limit the following seriesSolve limit with Riemann sum.Rearranging Limit ProblemLimit of a function with absolute valuesEvaluate the following limit without L'Hopitalevaluate the limit $lim_xto 2+frac[x]sin (x-2)(x-2)^2$Calculate the sum of a seriesDetermine whether the series $frace^frac1nn^2$ converges or divergesA limit involving irrational powers: can I use L'Hopital?Compute the limit as $t to 0$ of the given expressionLimit of a Sequence involving factorialsHow do you evaluate $lim_xtoinfty(x!*e^-x^2)$
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Evaluate the limit the following series
Solve limit with Riemann sum.Rearranging Limit ProblemLimit of a function with absolute valuesEvaluate the following limit without L'Hopitalevaluate the limit $lim_xto 2+frac[x]sin (x-2)(x-2)^2$Calculate the sum of a seriesDetermine whether the series $frace^frac1nn^2$ converges or divergesA limit involving irrational powers: can I use L'Hopital?Compute the limit as $t to 0$ of the given expressionLimit of a Sequence involving factorialsHow do you evaluate $lim_xtoinfty(x!*e^-x^2)$
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;
$begingroup$
Evaluate the limit $$lim_nto infty sum_j=1^n frac4j^2n^3.$$
I was under the assumption that this would just tend to $0$ after expanding everything because the denominator will grow quicker than the numerator, but apparently this is not the case.
sequences-and-series limits limits-without-lhopital
edited 8 hours ago
Bach
2,5652 gold badges9 silver badges24 bronze badges
asked 8 hours ago
WallaceWallace
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$endgroup$
add a comment |
$begingroup$
Evaluate the limit $$lim_nto infty sum_j=1^n frac4j^2n^3.$$
I was under the assumption that this would just tend to $0$ after expanding everything because the denominator will grow quicker than the numerator, but apparently this is not the case.
sequences-and-series limits limits-without-lhopital
edited 8 hours ago
Bach
2,5652 gold badges9 silver badges24 bronze badges
asked 8 hours ago
WallaceWallace
1587 bronze badges
$endgroup$
3
$begingroup$
The keyword is "Riemann sum". See for example math.stackexchange.com/questions/2712723/…?
$endgroup$
– Robert Z
8 hours ago
add a comment |
$begingroup$
Evaluate the limit $$lim_nto infty sum_j=1^n frac4j^2n^3.$$
I was under the assumption that this would just tend to $0$ after expanding everything because the denominator will grow quicker than the numerator, but apparently this is not the case.
sequences-and-series limits limits-without-lhopital
edited 8 hours ago
Bach
2,5652 gold badges9 silver badges24 bronze badges
asked 8 hours ago
WallaceWallace
1587 bronze badges
$endgroup$
Evaluate the limit $$lim_nto infty sum_j=1^n frac4j^2n^3.$$
I was under the assumption that this would just tend to $0$ after expanding everything because the denominator will grow quicker than the numerator, but apparently this is not the case.
sequences-and-series limits limits-without-lhopital
sequences-and-series limits limits-without-lhopital
edited 8 hours ago
Bach
2,5652 gold badges9 silver badges24 bronze badges
asked 8 hours ago
WallaceWallace
1587 bronze badges
edited 8 hours ago
Bach
2,5652 gold badges9 silver badges24 bronze badges
asked 8 hours ago
WallaceWallace
1587 bronze badges
edited 8 hours ago
Bach
2,5652 gold badges9 silver badges24 bronze badges
edited 8 hours ago
Bach
2,5652 gold badges9 silver badges24 bronze badges
edited 8 hours ago
Bach
2,5652 gold badges9 silver badges24 bronze badges
2,5652 gold badges9 silver badges24 bronze badges
asked 8 hours ago
WallaceWallace
1587 bronze badges
asked 8 hours ago
WallaceWallace
1587 bronze badges
asked 8 hours ago
WallaceWallace
1587 bronze badges
1587 bronze badges
3
$begingroup$
The keyword is "Riemann sum". See for example math.stackexchange.com/questions/2712723/…?
$endgroup$
– Robert Z
8 hours ago
add a comment |
3
$begingroup$
The keyword is "Riemann sum". See for example math.stackexchange.com/questions/2712723/…?
$endgroup$
– Robert Z
8 hours ago
3
3
$begingroup$
The keyword is "Riemann sum". See for example math.stackexchange.com/questions/2712723/…?
$endgroup$
– Robert Z
8 hours ago
$begingroup$
The keyword is "Riemann sum". See for example math.stackexchange.com/questions/2712723/…?
$endgroup$
– Robert Z
8 hours ago
add a comment |
2 Answers
2
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$begingroup$
Recognize the limit as the integral $$int _0^1 4x^2 dx $$
answered 8 hours ago
Mohammad Riazi-KermaniMohammad Riazi-Kermani
48.9k4 gold badges27 silver badges71 bronze badges
$endgroup$
add a comment |
$begingroup$
Note that $$sum_j=1^n j^2=fracn(n+1)(2n+1)6$$ we have
beginalign
lim_ntoinftysum_j=1^nfrac4j^2n^3&=lim_ntoinftyfrac2(n+1)(2n+1)3n^2\
&=frac23lim_ntoinfty(1+frac1n)(2+frac 1n)\
&=frac43.
endalign
answered 8 hours ago
BachBach
2,5652 gold badges9 silver badges24 bronze badges
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2 Answers
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2 Answers
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$begingroup$
Recognize the limit as the integral $$int _0^1 4x^2 dx $$
answered 8 hours ago
Mohammad Riazi-KermaniMohammad Riazi-Kermani
48.9k4 gold badges27 silver badges71 bronze badges
$endgroup$
add a comment |
$begingroup$
Recognize the limit as the integral $$int _0^1 4x^2 dx $$
answered 8 hours ago
Mohammad Riazi-KermaniMohammad Riazi-Kermani
48.9k4 gold badges27 silver badges71 bronze badges
$endgroup$
add a comment |
$begingroup$
Recognize the limit as the integral $$int _0^1 4x^2 dx $$
answered 8 hours ago
Mohammad Riazi-KermaniMohammad Riazi-Kermani
48.9k4 gold badges27 silver badges71 bronze badges
$endgroup$
Recognize the limit as the integral $$int _0^1 4x^2 dx $$
answered 8 hours ago
Mohammad Riazi-KermaniMohammad Riazi-Kermani
48.9k4 gold badges27 silver badges71 bronze badges
answered 8 hours ago
Mohammad Riazi-KermaniMohammad Riazi-Kermani
48.9k4 gold badges27 silver badges71 bronze badges
answered 8 hours ago
Mohammad Riazi-KermaniMohammad Riazi-Kermani
48.9k4 gold badges27 silver badges71 bronze badges
answered 8 hours ago
Mohammad Riazi-KermaniMohammad Riazi-Kermani
48.9k4 gold badges27 silver badges71 bronze badges
48.9k4 gold badges27 silver badges71 bronze badges
add a comment |
add a comment |
$begingroup$
Note that $$sum_j=1^n j^2=fracn(n+1)(2n+1)6$$ we have
beginalign
lim_ntoinftysum_j=1^nfrac4j^2n^3&=lim_ntoinftyfrac2(n+1)(2n+1)3n^2\
&=frac23lim_ntoinfty(1+frac1n)(2+frac 1n)\
&=frac43.
endalign
answered 8 hours ago
BachBach
2,5652 gold badges9 silver badges24 bronze badges
$endgroup$
add a comment |
$begingroup$
Note that $$sum_j=1^n j^2=fracn(n+1)(2n+1)6$$ we have
beginalign
lim_ntoinftysum_j=1^nfrac4j^2n^3&=lim_ntoinftyfrac2(n+1)(2n+1)3n^2\
&=frac23lim_ntoinfty(1+frac1n)(2+frac 1n)\
&=frac43.
endalign
answered 8 hours ago
BachBach
2,5652 gold badges9 silver badges24 bronze badges
$endgroup$
add a comment |
$begingroup$
Note that $$sum_j=1^n j^2=fracn(n+1)(2n+1)6$$ we have
beginalign
lim_ntoinftysum_j=1^nfrac4j^2n^3&=lim_ntoinftyfrac2(n+1)(2n+1)3n^2\
&=frac23lim_ntoinfty(1+frac1n)(2+frac 1n)\
&=frac43.
endalign
answered 8 hours ago
BachBach
2,5652 gold badges9 silver badges24 bronze badges
$endgroup$
Note that $$sum_j=1^n j^2=fracn(n+1)(2n+1)6$$ we have
beginalign
lim_ntoinftysum_j=1^nfrac4j^2n^3&=lim_ntoinftyfrac2(n+1)(2n+1)3n^2\
&=frac23lim_ntoinfty(1+frac1n)(2+frac 1n)\
&=frac43.
endalign
answered 8 hours ago
BachBach
2,5652 gold badges9 silver badges24 bronze badges
answered 8 hours ago
BachBach
2,5652 gold badges9 silver badges24 bronze badges
answered 8 hours ago
BachBach
2,5652 gold badges9 silver badges24 bronze badges
answered 8 hours ago
BachBach
2,5652 gold badges9 silver badges24 bronze badges
2,5652 gold badges9 silver badges24 bronze badges
add a comment |
add a comment |
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The keyword is "Riemann sum". See for example math.stackexchange.com/questions/2712723/…?
$endgroup$
– Robert Z
8 hours ago