calculus ....... answer in detail?

Question

explain why lim x approaching infinity mx + b / x^2 +5x +1 = 0 for any m, b is rational number.

Answer 1

The degree of the denominator (highest power of x) is 2 while the degree of the numerator is 1. The bottom will grow much faster than the top.

Answer 2

I've added parentheses. I assume you mean the limit of
(mx + b) / (x² +5x +1) = 0 as x→∞.

Divide each term in the numerator and denominator by x². Then you have:

lim x→∞ of (m/x + b/x²) / (1 +5/x +1/x²) = (0 + 0)/(1 + 0 + 0) = 0

So the limit is 0 for any constants m and b and is therefore a rational number. The limit will equal zero as x→∞ whenever the denominator is a higher degree polynomial than the numerator.

Answer 3

The degree of the denominator (highest power of x) is 2 while the degree of the numerator is 1. The bottom will grow much faster than the top.

lim x approaching infinity mx + b / x^2 +5x +1 = 0 for any m, b is rational number.
Here is a simpler limit where we can see what is being approached.
lim
x1
x2 1
x1 =2
While this limit expression is also only defined for 0 <|x1|, or x
= 1,themystery is
easily resolved with a little algebra,
x2 1
x1 = (x1)(x+1)
(x1) =x+1
So,
lim
x1
x2 1
x1 = lim
x1(x+1)=2
The limit limx1(x+ 1) = 2 is so obvious as to not need a technical definition. If x is
nearly 1, then x+ 1 is nearly 1 + 1 = 2. So, while this simple example illustrates that the
original expression does get closer and closer to 2 as x gets closer and closer to 1, it skirts
the issue of how close?

Answer 4

What happens when you multiply top an and bottom of this fraction by 1/x^2? Note this won't change your answer because you are just multiplying by 1 as long as x is not 0.

Answer 5

ok...
you can divide everything by x
look....
(mx/x + b/x)/ (x.x/x + 5.x/x + 1/x)....then cancel out the x's and when there is a number divided x ....it will go to zero...the it will cancel out...
it will give you ....
(m + 0)/ (x +5 + 0)= m/x+5......x could be any number and m is a constant...
therefore the limit will go to zero...

Answer 6

a) All you will desire to do is plug in however your t is into the formula. as an occasion, if t = 3, then you particularly would plug it into the formula like this: N(3) = one thousand(3)^3/one hundred(3^3) and remedy. b) what's seen totally developed? Is it one thousand homes, a hundred thousand homes, or 3 homes?