Question

Prove : 0/0 =2 need a VERIFIED answer ​and correct answer too

Answer 1

Answer

0/0

is specifically called an indeterminant form.

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]

Saumyaa Srivastava

Answered April 19, 2018

A single value can’t be assigned to a fraction where the denominator is [math]0[/math], so the value remains undefined. Division by [math]0[/math] is undefined in mathematics.

[math]0÷0[/math] is known as indeterminate.

If [math]0/0[/math] can be [math]2[/math], then [math]0/0[/math] can be written as 3, 4, 67, 163892, 2819010 and what not.

Infact, [math]0/0[/math] can be any number.

But just for the sake of question:

Let, [math]0/0 = 81-81/81-81[/math]

[math]=> 0/0 = 81-81/81-81[/math]

[math]=> 0/0 = 9^2-9^2/9^2-9^2[/math]

[math]=> 0/0 = (9+9)(9-9)/9(9-9)[/math]

Since, [math]a^2-b^2 = (a+b)(a-b)[/math]

[math]=> 0/0 = (9+9)/9 = 18/9[/math]

[math]=> 0/0 = 2[/math]

Hence, [math]0/0 = 2[/math]

Answer 2

QuestioN :

Prove : 0/0 =2

GiveN :

• 0/0 =2

To FiNd :

• Prove

SolutioN :

By solving L.H.S Part we get,

$=\frac{0}{0} \\\\=\frac{(100-100)}{100-100)} \\\\=\frac{(10)^2-(10)^2}{10(10-10)}$

By using : a² - b² = ( a + b) (a -b)

$=\frac{(10+10)(10-10)}{10(10-10)}$

$=\frac{10+10}{10} \\\\=\frac{20}{10} \\\\=2$

Here we found,

L.H.S = 2

R.H.S = 2

Therefore,

L.H.S = R.H.S

HENCE PROVED