Define the value of 0 in the infinite terms of no. ?
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Let us assume a function called f(x)=1/g(x)
Lets assume g(a)=0 where a is some real value.
So what we need to prove is f(a)=∞
case 1 : g(a)=0 and g′(a)=+ve, then in this case g(a+δ)=+ve and
g(a−δ)=−ve, where δ→0+
Thus f(a+δ)=1/g(a+δ)=+∞,
And f(a−δ)=1/g(a−δ)=−∞
Thus f(a) approaches +∞ from one side and −∞ from other side. So exactly at f(a) we won’t be able to say, whether it is +∞ or −∞, so in this case we should say 1/0 is undefined.
Let us assume a function called f(x)=1/g(x)
Lets assume g(a)=0 where a is some real value.
So what we need to prove is f(a)=∞
case 1 : g(a)=0 and g′(a)=+ve, then in this case g(a+δ)=+ve and
g(a−δ)=−ve, where δ→0+
Thus f(a+δ)=1/g(a+δ)=+∞,
And f(a−δ)=1/g(a−δ)=−∞
Thus f(a) approaches +∞ from one side and −∞ from other side. So exactly at f(a) we won’t be able to say, whether it is +∞ or −∞, so in this case we should say 1/0 is undefined.
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I don't know this ans so sorry
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