Question

Guys this is a tricky one. so the correct answer will be marked as brainliest.

prove that 0/0=2. ​

Answer 1

Answer:

Any division by zero is undefined but 

0/0 is different from nonzero number/0 

because if a is not zero and we try to 

write x= a/0 , if it were definable then it 

would satisfy

0x = a

and there is no such x.

However,

if a=0

the equation

0x =0 is true

for EVERY REAL NUMBER, and is in fact true for EVERY COMPLEX NUMBER!!!

That is the reason we call it indeterminant instead of undefined.

The fact that it is indeterminant leads to some 

interesting and wonderful results you get to 

study at the second or third Calculus level.

In particular, if an expression f(x)/g(x) is of the 

form where f(x) gets closer and closer to zero 

and g(x) gets closer to zero as x gets closer to 

some number, there is a rule for figuring out 

what f(x)/g(x) gets closer to or approaches.

If g(x) gets closer and closer to zero as 

x gets closer and closer to a number such 

as 5, then at the calculus level we say 

limit as x gets closer and closer to 5 of g(x) 

equals zero. The expression 2x -10 is 

an expression which gets closer and closer 

to zero as x gets closer to 5. Likewise 

f(x)=x² - 25 gets closer and closer to 0 as 

x gets closer to 5.

Consider f(x)/g(x) = (4x² - 100)/(2x- 10)

If we let x get closer and closer to 5 we can 

see that f(x)/g(x) gets closer, in form to 0/0 .

In a first calculus course, we would factor 

the numerator 

and figure it equals 4(x-5)(x+5) and denominator 

equals 2(x-5)

and since (x-5)/(x-5) equals 1 for all x not equal to 5 we assume it stays equal to 1 as x gets closer to zero and cancel them, obtaining 

f(x)/g(x) = 4(x + 5)/2 , substitute in 5 and 

figure out that 4(x + 5)/2 gets closer and 

closer to 4(10)/2 = 20 as x gets closer to 5.

The 2nd or 3rd calculus course lets you prove 

that using L'Hôpital's Rule for 0/0 type expressions that 

as f(x)/g(x) gets closer and closer to a 0/0 

form as x gets closer to 5 then 

the expression gets closer in value to 

f'(x)/g'(x) called the ratio of the derivatives.

You will learn what a derivative is in Calculus 

For this example it is 8x/2 and we evaluate 

this at x=5 to show it has a value of 20 .

Here 0/0 equals 20. However it does not always 

equal 20. It can equal ANY REAL NUMBER.

That's the reason we call it indeterminate 

[ Value not determined] 

rather than simply undefined where 

[The value does not exists]