Find the limit?

Question

Lim ->infinity (2x+5)/(1-x)

Lim ->infinity (a-bx^4)/(cx^4 + x^2)

Answer 1

Le Chatelier's Principle is a statement about the stability of equilibria in physical systems. He means L'Hopital's rule, which looks for proportionalities in growth rates, treating all noninfinite constants as negligible. The growth rates are the derivatives, so the rule is to take the derivative of the top and of the bottom. You may have to take the limit after forming this ratio.

His answers are right:
d/dx(2x+5)=2
d/dx(1-x)=-1
=>2/-1=-2

d/dx(a-bx^4)=-4bx^3
d/dx(cx^4+x^2)=4cx^3+2x
=>-4bx^3/(4cx^3+2x)
divide top and bottom by 4x^3
=>-b/(c+1/(2x))
The limit of which as x->infty is -b/c

Answer 2

Lim ->infinity (2x+5)/(1-x) =
Lim ->infinity (2+5/x)/(1/x -1) =
(2+0)/(0 -1) = -2

Lim ->infinity (a-bx^4)/(cx^4 + x^2) =
Lim ->infinity (a/x^4 - b)/(c + 1/x^2) =
(0 - b)/(c + 0) = -b/c

Th

Answer 3

Lt x--infinity(2x+5)/(1-x)

=lt x--infinity {2+1/x}/[1/x-1] --------(1)

we know that as x->infinity ; 1/x->0

=>(1) = lt 1/x-->0 {2+1/x}/{1/x-1}

={2+0}/{0-1}

=2/-1

= -2 Ans.

Answer 4

-2 and -b/c

Answer 5

answers:
1. x= infinity
2. x= infinity

Answer 6

Use Le'Chatlier's Principle, since each of these are indeterminant (inf/inf). Take the derivitive of the num and denom until no longer indeterminant to get:

1. -2

2. -b/c

Answer 7

when x is really large and approaches infinity then

1) 2x/(-x) = -2

2) (-bx^4)/(cx^4) = -b/c

Answer 8

I believe the limit is 1.5
That is such a nice number.