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Lebl-Basic-Analysis-I
· Problem 6.2.4
Sequences of Functions
Mathematics · limit-of-integral-exponential
Problem
Show
lim
n
→
∞
∫
1
2
e
−
n
x
2
d
x
=
0
\displaystyle\lim_{n\to\infty} \int_1^2 e^{-nx^2}\, dx = 0
n
→
∞
lim
∫
1
2
e
−
n
x
2
d
x
=
0
. Feel free to use calculus facts about the exponential.
Related theory
Limit Superior And Limit Inferior
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