A Burst of Colorful Spring Flowers

[LasTSurvivoR]

http://img501.imageshack.us/img501/2654/z5jc.jpg"
thx.

 

[NateTG]

http://img501.imageshack.us/img501/2654/z5jc.jpg"
thx.

Looks like this belongs in the homework section.

Are you familiar with l'Hospital's rule?

 

[LasTSurvivoR]

yup i knew it , but how can we use it here ? no 0 / 0 or everlasting / everlasting ?


/ Sry didnt saw homework sec

 

[NateTG]

No worries, just use the homework section next time.

It's beena little while, but:
$$0^\infty$$
and
$$\infty^0$$
are also places that you can apply l'Hospitals rule.
Let's say we have two functions:
$$\lim_{x \rightarrow y} f(x) \rightarrow 0$$
and
$$\lim_{x \rightarrow y} g(x) \rightarrow \infty$$

Then
$$\lim_{x \rightarrow y} g(x)^{f(x)}=\lim_{x \rightarrow y} e^{f(x) \ln(g(x))}$$
And the exponent there is of the form:
$$0 \times \infty$$

 

[shmoe]

You don't need to use l'hopital. Try pulling out the 7*8^n from inside the ().

 

[LasTSurvivoR]

NateTg i understand what you meant.Thanks.

 

[LasTSurvivoR]

But can't solve that : e ^ [ 2 / n . ln ( 5^n + 7.8^n ) ]

What should i do e ^ ( fx . gx ) now ?

 

[NateTG]

Well the limit of the exponent is the exponent of the limit, but you're better off using shmoe's technique.

 

[Alkatran]

The first thing that jumps into my head is that the limit, if you remove the 5^n, is simply 7.8^(n*2/n) = 60.84. So, since we've ignored adding 5^n before rooting, the answer must be at least 60.84.

There's only one answer that satisfies that, clearly demonstrating why I love multiple choice tests so much.

 

[StatusX]

I think that's supposed to be 7*8^n, otherwise none of the choices are correct.

 

[BoTemp]

n's going to infinity right? Easy way is piecewise. 7*8^n >> 5^n as n => infinity, so that term can be neglected (basically same is dividing out the 7*8^n, just slightly quicker and less rigorous). You get 7^(2/n)*(8^n)^(2/n) => 8^2 = 64.

 

[Robokapp]

I don't understand the question...I don't see any lim (x->something)

Do you mean maximum value? or the limit as x approaches infinity?

(5^2n + 5^n * 14 * 8^n + 49 * 8 ^2n) under a n-th radical...

I won't lie i don't know but my TI-84 does :D