what is 5 + 5 x infinity / (0 x 1 + infinity)?

Answer 1

The question is meaningless because infinity is not a number.

ASIDE TO bablunt: Your limit works only of the top and bottom infinities are converging at the same rate. There is no guarantee of this, so the correct way to formulate your limit would be as follows:

. . . lim . . . 5 + 5x / (0*1 + y)
(x,y) →(∞,∞)

And for that expression the limit is undefined.

Answer 2

It is very important to remember that infinity is not a real number so we cannot apply all the properties of the arithmetic of real numbers when working with infinity.

For your problem, the numerator is infinity as well as the denominator. So, you have an expression of the form infinity/infinity, which is called an indeterminate form because it does not have a specific value.

It can be hard to see why the result is not a specific real number. To try to understand, we suppose that it were a specific real number, say x.

Then, we'd have

infinity/infinity=x

so

infinity=infinity times x

All nonzero numbers satisfy this equation: the equation does not have a unique (single) solution. That is, x is not determined by the expression--so the expression is said to be "undefined."

Working with infinity can be problematic since it is not a real number. infinity+infinity=infinity but infinity-infinity is indeterminate. Similarly, 0/0 is indeterminate even though 0 times 0 equals 0. Division by 0 is always undefined. On the other hand, 0 divided by any nonzero number is always 0.

Solving equations is always the thing in math: if your answer has a unque (exactly one) solution, then you have solved your problem. Sometimes, there is no answer or the answer is not unique so we say that the question is illdefined, indeterminate, not known, etc...

Answer 3

Solve,

(5 + 5 x infinity) / (0 x 1 + infinity)

Note:

5 + 5 x infinity = infinity

and

0 x 1 + infinity = infinity

Therefore, taking limits,

infinity/infinity = 1

Answer 4

5

Answer 5

5+5=10
10 X infinity = infinity again.

0 X 1 = 0
0 + infinity = infinity

then, infinity / infinity = 1

isn't it right ? :-)

Answer 6

If this were a limit problem it could probabably be worked. As it is, the infinities are working against each other and we say it is of an indeterminate form. You don't apply limits if its not in the problem. Infinity over infinity is not one. You need to investigate cardinal numbers.

Answer 7

Depends it could be 10 or infinity (square) x 5 + 5 or infinity x 5 x infinity + 5 depends on how you would put them in order PEMDAS

Answer 8

10

Answer 9

As you wrote it,
5 + 5*inf./(0*1+inf.)
The people who said 10 are exactly correct.
You solve these by as a limit

5 + 5*x/x since 0*1 + x = x
Then let x go to infinity.

At each stage of the limit forever, the x/x is 1 so you get
5 + 5 = 10

If you have a plotting program (or by hand ;-)
plot the equation with the x in it (as above) and you will
see if you go out far enough the line approaches 10.

Answer 10

let infinity = x
your qn. is
lim x-> infinity 5+ 5x/(0*1 + x)
= lim x-> infinity 5+5x/(x)
=5+5 =10