Limits doubt
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
9 Replies
@Apu
Note for OP
+solved @user1 @user2... to close the thread when your doubt is solved. Mention the users who helped you solve the doubt. This will be added to their stats.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
@Opt any insights?
Give me an example please
Say (x-2)(x-3)/(x-2)(x-5)
Well, that function behaves exactly like (x-3)/(x-5) everywhere but at x=2 where it has a point discontinuity
limit exists if f(a-)=f(a+) right
f(a) neednt be defined
like here
(take a=2 here)
it wont be continous but it will have a limit
O I see
I messed up thinking that the graphical transform would result in a different function,kind of like sinx and sinx + k
+solved @Opt @Augustine
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