Dtjytyk

Can the harmonic series explain the origin of the major scale?

Superhero words!

Can I rely on these GitHub repository files?

Are taller landing gear bad for aircraft, particulary large airliners?

Is a naturally all "male" species possible?

Is there a problem with hiding "forgot password" until it's needed?

What was required to accept "troll"?

Simple image editor tool to draw a simple box/rectangle in an existing image

Books on the History of math research at European universities

Java - What do constructor type arguments mean when placed *before* the type?

Is there an Impartial Brexit Deal comparison site?

For airliners, what prevents wing strikes on landing in bad weather?

Calculating the number of days between 2 dates in Excel

Blender - show edges angles “direction”

Simulating a probability of 1 of 2^N with less than N random bits

I'm in charge of equipment buying but no one's ever happy with what I choose. How to fix this?

What (else) happened July 1st 1858 in London?

Why does this part of the Space Shuttle launch pad seem to be floating in air?

Hostile work environment after whistle-blowing on coworker and our boss. What do I do?

Proof of Lemma: Every integer can be written as a product of primes

How will losing mobility of one hand affect my career as a programmer?

Can I create an upright 7-foot × 5-foot wall with the Minor Illusion spell?

Why is delta-v is the most useful quantity for planning space travel?

Does "Dominei" mean something?

Support of integrand vanishing?

Integrand becomes infinite when length of interval goes to zeroSuperior limit of integrals of entire functionsWhich negation of the definition of a null sequence is correct?Prove if $f(0) = 0$ then $lim_{x to 0^+}xint_x^1 frac{f(t)}{t^2}dt = 0$ for regulated function $f$Limit of a sequence in an $L^{p}$ space.Open problem in math that just needs differentiationProve $lim_{xto a} frac{f(x)}{g(x)} =0$How do $int_0^{infty} leftlvert f(x) rightrvert dx $ and $int_0^{infty}int_0^{infty} leftlvert f(x+y) rightrvert dx dy$ compare?Uniform continuity of $xlog(x)$Confusion in a Proof

1

1

$begingroup$

Consider the integral

$$f(y)=int_{mathbb R} e^{-(x-y)^4} e^{-x^2} dx.$$

For every $varepsilon>0$ and every $y$ there exists a smallest interval $I_y$ such that

$$leftlvert f(y)^{-1}int_{I_y} e^{-(x-y)^4} e^{-x^2} dx- 1 rightrvert ge 1-varepsilon.$$

I would like to ask: What can be said about the length of the interval $I_y$ as $y rightarrow infty.$

Does the length go to zero, as $y$ tends to infinity.

real-analysis calculus integration analysis

share|cite|improve this question

asked Mar 14 at 20:32

SaschaSascha

88318

$endgroup$

add a comment | 

1

1

$begingroup$

Consider the integral

$$f(y)=int_{mathbb R} e^{-(x-y)^4} e^{-x^2} dx.$$

For every $varepsilon>0$ and every $y$ there exists a smallest interval $I_y$ such that

$$leftlvert f(y)^{-1}int_{I_y} e^{-(x-y)^4} e^{-x^2} dx- 1 rightrvert ge 1-varepsilon.$$

I would like to ask: What can be said about the length of the interval $I_y$ as $y rightarrow infty.$

Does the length go to zero, as $y$ tends to infinity.

real-analysis calculus integration analysis

share|cite|improve this question

asked Mar 14 at 20:32

SaschaSascha

88318

$endgroup$

add a comment | 

$begingroup$

Consider the integral

$$f(y)=int_{mathbb R} e^{-(x-y)^4} e^{-x^2} dx.$$

For every $varepsilon>0$ and every $y$ there exists a smallest interval $I_y$ such that

$$leftlvert f(y)^{-1}int_{I_y} e^{-(x-y)^4} e^{-x^2} dx- 1 rightrvert ge 1-varepsilon.$$

I would like to ask: What can be said about the length of the interval $I_y$ as $y rightarrow infty.$

Does the length go to zero, as $y$ tends to infinity.

real-analysis calculus integration analysis

share|cite|improve this question

asked Mar 14 at 20:32

SaschaSascha

88318

$endgroup$

share|cite|improve this question

asked Mar 14 at 20:32

SaschaSascha

88318

share|cite|improve this question

asked Mar 14 at 20:32

SaschaSascha

88318

asked Mar 14 at 20:32

SaschaSascha

88318

asked Mar 14 at 20:32

SaschaSascha

88318