What would be the result of the following divisions?
depending on what course you are taking, you can use limits to solve most of these, but if not, you simply say they do not exist.
a. 1/0 Divide by 0, does not exist
b. 1/INFINITY does not exist
c. INFINITY/0 divide by 0, does not exist
d. 0/INFINITY = 0 (0 divided by anything is 0)
e. INFINITY/1 = INFINITY (dividing in 1 piece is just itself)
f. INFINITY/INFINITY = 1 (x/x is always 1)
g. 0/0 = divide by 0, does not exist
a.) 1/0 = infinity (any positive real number divided by zero is infinity)
b.) 1/infinity = 0 (any real number divided by infinity is zero)
c.) infinity/0 = infinity
say, infinity = r/0, where r = a positive real number
so... (r/0) / 0 = r / (0*0) = infinity
d.) 0/infinity = 0
0 / (r/0) = (0 * 0)/r = 0
e.) infinity/1 = infinity
(Divide infinity by any positive number and you obtain infinity. Divide infinity by any negative number and you obtain negative infinity.)
f.) infinity/infinity = indeterminate
say, infinity in the numerator = r/0. denominator = s/0, wherein s = a positive real number
so... (r / 0) / (s / 0) = r/s
But what is r/s? It can be any rational number. So the answer is indeterminate.
g.) 0/0 = indeterminate
say, numerator = r*0, denominator = s*0
so... (r*0) / (s*0) = r/s
Again, r/s can be any rational number. Hence, indeterminate.