Limits doubt | iTeachChem | Page 1

strange trail Jun 9, 2025, 11:42 AM

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While solving limits, we sometime factor out and cancel some terms from numerator and denominator. However doesnt that fundamentally change the function. As we cancel terms, we change how it looks on a graph so shouldnt it change the function itself for which we are calculating limit

left orchidBOT Jun 9, 2025, 11:43 AM

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Note for OP

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strange trail Jun 9, 2025, 11:45 AM

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One explanation ive been given is that while solving limits, we only care about the neighbourhood of the function so cancelling out factors isnt a big deal

however, won't cancelling factors also change the neighbourhood and hence, the limit

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@light zenith any insights?

light zenith Jun 9, 2025, 12:16 PM

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strange trail One explanation ive been given is that while solving limits, we only care about ...

Give me an example please

strange trail Jun 9, 2025, 12:17 PM

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Say (x-2)(x-3)/(x-2)(x-5)

light zenith Jun 9, 2025, 1:03 PM

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Well, that function behaves exactly like (x-3)/(x-5) everywhere but at x=2 where it has a point discontinuity

exotic granite Jun 9, 2025, 2:22 PM

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limit exists if f(a-)=f(a+) right

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f(a) neednt be defined

exotic granite Jun 9, 2025, 2:23 PM

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strange trail Say (x-2)(x-3)/(x-2)(x-5)

like here

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(take a=2 here)

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it wont be continous but it will have a limit

strange trail Jun 9, 2025, 2:24 PM

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light zenith Well, that function behaves exactly like (x-3)/(x-5) everywhere but at x=2 where...

O I see
I messed up thinking that the graphical transform would result in a different function,kind of like sinx and sinx + k

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+solved @light zenith @exotic granite

#Limits doubt