Find (lt_{x rightarrow infty}(( frac{x^3+x^2+x}{x^3+x+1})^{x+3}) )

1.	Find (lt_{x rightarrow infty}(( frac{x^3+x^2+x}{x^3+x+1})^{x+3}) )
A.	e
B.	e<sup>-1</sup>
C.	0
D.	1
Answer» B. e<sup>-1</sup>

Discussion

Find (=lt_{x rightarrow 0} frac{(a_nx^n+a_{n-1}x^{n-1}+ +a_1x+a_0)}{(b_nx^n+b_{n-1}x^{n-1}+ +b_1x+b_0)} )
Find (lt_{x rightarrow 0} frac{sin(sin(x))}{x} )
Find (lt_{x rightarrow 0} frac{sin((4x^3)tan^{-1}(x))}{x^4} )
Find (lt_{x rightarrow -5}( frac{tan^{-1}(x^2+6x+5)}{x^2+15x+50}) )
Find (lt_{x rightarrow -101}( frac{ln(x^2+20x+(x+101)^2(x^2+3))-ln(x^2+20x)}{x^2+202x+10201}) ).
Find (lt_{n rightarrow infty} frac{(1^a+2^a+ +(n-1)^a)}{n^{a+1}} )
Find (lt_{n rightarrow infty} sum_{a=1}^{n-1}( frac{ln(1+ frac{a}{n})}{n}) )
Find (lt_{x rightarrow -2}( frac{sin((x-2)^2)}{(x+2)^2}) )
Find (lt_{x rightarrow infty}(( frac{x^3+x^2+x}{x^3+x+1})^{x+3}) )
Find (lt_{x rightarrow 0}( frac{1}{sin^2(x)}) )