Limit Infinity Question

[Jason76]

Where \(\displaystyle n = \) a real number

\(\displaystyle n - \infty = ?\)

\(\displaystyle n + \infty = ?\)

\(\displaystyle \infty + n = ?\)

\(\displaystyle \infty - n = ?\)

\(\displaystyle \infty - \infty = ?\)

\(\displaystyle \dfrac{\infty}{n} = ?\)

\(\displaystyle \dfrac{\infty}{0} = ?\)

\(\displaystyle \infty + 0 = ?\)

\(\displaystyle 0 + \infty = ?\)

Here are some I already know:

\(\displaystyle \dfrac{0}{0} =\) Indeterminate

\(\displaystyle \dfrac{0}{\infty} = 0\)

\(\displaystyle \dfrac{n}{\infty} = 0\)

\(\displaystyle \dfrac{\infty}{\infty} = \infty\)

\(\displaystyle (\infty)(\infty) = \infty\)

\(\displaystyle (n)(\infty) = \infty\)

\(\displaystyle (0)(\infty) = \) Indeterminate

\(\displaystyle 0 - \infty = -\infty\)

\(\displaystyle \infty - 0 =\) Indeterminate

\(\displaystyle \infty + \infty = \infty\)

 

[DrPhil]

Where \(\displaystyle n = \) a real number

\(\displaystyle n - \infty = ?\)

\(\displaystyle n + \infty = ?\)

\(\displaystyle \infty + n = ?\)

\(\displaystyle \infty - n = ?\)

\(\displaystyle \infty - \infty = ?\)

\(\displaystyle \dfrac{\infty}{n} = ?\)

\(\displaystyle \dfrac{\infty}{0} = ?\)

\(\displaystyle \infty + 0 = ?\)

\(\displaystyle 0 + \infty = ?\)

Here are some I already know:

\(\displaystyle \dfrac{0}{0} =\) Indeterminate

\(\displaystyle \dfrac{0}{\infty} = 0\)

\(\displaystyle \dfrac{n}{\infty} = 0\)

\(\displaystyle \dfrac{\infty}{\infty} = \infty\)... NO

\(\displaystyle (\infty)(\infty) = \infty\)

\(\displaystyle (n)(\infty) = \infty\)

\(\displaystyle (0)(\infty) = \) Indeterminate

\(\displaystyle 0 - \infty = -\infty\)

\(\displaystyle \infty - 0 =\) Indeterminate... NO

\(\displaystyle \infty + \infty = \infty\)

Guess the others?

HINT: only ONE of them is indeterminate.

 

[daon2]

Zero times infinity is sometimes defined to be zero. It depends on the context. For limits you are correct, it is treated as indeterminate

 

[Jason76]

Zero times infinity is sometimes defined to be zero. It depends on the context. For limits you are correct, it is treated as indeterminate

Please give me an example of a context where it evaluates to 0, and when infinity.