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Find $alpha, beta$ and nonzero $a_1, a_2$ for the following function

How to prove that $lim_ntoinftybig(1+1/nbig)^n$ is equal to eFind the limit of a multivariable function that's a quotient of polynomials: $f(x)=fracx^3y^3x^2+y^2$$f(alpha x)-f(beta x) to 0$ faster than $frac1log x$ for all functions $f$Show that the limit of $fracsin(x) - sin(y)x+y$ does not exist.Proof of limit of $left(sqrtn+1-sqrtnright)left(sqrtn+frac12right)=frac12$How do I calculate this limit when two terms tend to infinity at similar ratesLimit of $(s_1 + ldots + s_n)/n$If $a_1 = 3$ and $a_n+1=a_n^2-2$, then $dfrac1a_1+dfrac1a_1a_2+dfrac1a_1 a_2 a_3+cdots = dfrac3-sqrt52.$Let $alpha,beta in mathbbR$ then find conditions for when $limlimits_(x,y)rightarrow(0,0)fracx^alphay^betax^2+xy+y^2$ exists.

-1

$begingroup$

I need to solve the following exercise:

Exercise: Assuming $fsim a_1epsilon^alpha + a_2epsilon^beta + ldots,$ find $alpha,beta$ (with $alpha < beta)$ and nonzero $a_1,a_2$ for the following function:
$$
f = (1+epsilon x)^1/epsilon, text for 0<x<infty
$$
What I've tried so far: I need an expression for $a_1,a_2,$ so I tried to take the limit:
$$
a_1 = lim_epsilonto 0dfrac(1+epsilon x)^1/epsilonepsilon^alpha
$$
but this doesn't really get me anywhere..

Question: Does someone have some hints on how to solve this exercise? Thanks in advance!

limits approximation

share|cite|improve this question

asked Mar 12 at 10:58

TitusTitus

424

$endgroup$

add a comment | 

-1

$begingroup$

I need to solve the following exercise:

Exercise: Assuming $fsim a_1epsilon^alpha + a_2epsilon^beta + ldots,$ find $alpha,beta$ (with $alpha < beta)$ and nonzero $a_1,a_2$ for the following function:
$$
f = (1+epsilon x)^1/epsilon, text for 0<x<infty
$$
What I've tried so far: I need an expression for $a_1,a_2,$ so I tried to take the limit:
$$
a_1 = lim_epsilonto 0dfrac(1+epsilon x)^1/epsilonepsilon^alpha
$$
but this doesn't really get me anywhere..

Question: Does someone have some hints on how to solve this exercise? Thanks in advance!

limits approximation

share|cite|improve this question

asked Mar 12 at 10:58

TitusTitus

424

$endgroup$

add a comment | 

$begingroup$

I need to solve the following exercise:

Exercise: Assuming $fsim a_1epsilon^alpha + a_2epsilon^beta + ldots,$ find $alpha,beta$ (with $alpha < beta)$ and nonzero $a_1,a_2$ for the following function:
$$
f = (1+epsilon x)^1/epsilon, text for 0<x<infty
$$
What I've tried so far: I need an expression for $a_1,a_2,$ so I tried to take the limit:
$$
a_1 = lim_epsilonto 0dfrac(1+epsilon x)^1/epsilonepsilon^alpha
$$
but this doesn't really get me anywhere..

Question: Does someone have some hints on how to solve this exercise? Thanks in advance!

limits approximation

share|cite|improve this question

asked Mar 12 at 10:58

TitusTitus

424

$endgroup$

share|cite|improve this question

asked Mar 12 at 10:58

TitusTitus

424

share|cite|improve this question

asked Mar 12 at 10:58

TitusTitus

424

asked Mar 12 at 10:58

TitusTitus

424

asked Mar 12 at 10:58

TitusTitus

424