limits showed me my limit

[jeeadvanceaspirant]

i tried replacing 1+x^2=e^x^2 that is the most common step my friend also did ....then the expresion was x^x^2/e^x^3 ...and obv we cant do l hospital now...i went on further and took log on b.s(idk if this is correct step or not as i have use log only in limits where 0^0 or infinity^0 were present. and then i got (lnx-x)/(1/x^2) which is 0/0 form and we get infinity as last ans and hence taking antilog we got infinity as final ans........also when i saw the graph of the function it was flat at infinity and 0 so if u get any lead please reply it will be great help

 

[Dr.Peterson]

i tried replacing 1+x^2=e^x^2 that is the most common step my friend also did ....then the expresion was x^x^2/e^x^3 ...and obv we cant do l hospital now...i went on further and took log on b.s(idk if this is correct step or not as i have use log only in limits where 0^0 or infinity^0 were present. and then i got (lnx-x)/(1/x^2) which is 0/0 form and we get infinity as last ans and hence taking antilog we got infinity as final ans........also when i saw the graph of the function it was flat at infinity and 0 so if u get any lead please reply it will be great helpView attachment 26850

The graph seems to show clearly that the limit is 0, not e^{1/2}. So something is wrong with the problem. It is also written oddly, so I wonder if there is a typo.

I don't understand what you are saying you did; but nothing valid that you do can change 0 to something else.

 

[jeeadvanceaspirant]

The graph seems to show clearly that the limit is 0, not e^{1/2}. So something is wrong with the problem. It is also written oddly, so I wonder if there is a typo.

I don't understand what you are saying you did; but nothing valid that you do can change 0 to something else.

yes agreed ! limit calculator also showed zero

 

[Dr.Peterson]

I tried graphing modified functions, and it looks like [MATH]\lim_{x\to\infty}\frac{e^x}{\left(1+\frac{1}{x}\right)^{x^2}}[/MATH] has the right limit, at least. Try working that out.