2 questions :) (1 Viewer)

[Snowe]

Hey guys have 2 questions

1) How do I solve (x+4)^4= 0?


Never seen this question before o.0



2) How do I find the limit of lim (x^2+3)/ (x+4) ?
x-> infinity


I know if it was a no. you would just substitute that no. inside because if you use a no. very close to that no. it would approach the no. being substituted but with the infinity its confusing o.0;

 

[Xayma]

1)
(x+4)⁴=0
∴
(x+4)=⁴√0
=0
∴
x=-4

2) lim (x--> ∞ ) (x²+3)/(x+4)
=lim (x--> ∞ ) (x²-16+19)/(x+4)
=lim (x--> ∞ ) (x²-16)/(x+4) +19/(x+4)
=lim (x--> ∞ ) (x+4)(x-4)/(x+4)+19/(x+4)
=lim (x--> ∞ ) (x-4)+19/(x+4)
as x--> ∞ 19/(x+4) --> 0
∴

lim (x--> ∞ ) (x^2+3)/(x+4)=x-4
which approaches &infin; as x--> &infin; the graph y=(x<sup>2</suP>+3)/(x+4) will approach y=x-4 as x--> &infin;

 

[Estel]

by inspection the expression approaches infinity anyhow as the power of the numerator > power of the denominator.

 

[Snowe]

Hey man thanks heaps for the working out