Question

pls explain: limit as x goes to 1

Answer 1

DNE

Answer 2

yes, but why exactly?

Answer 3

that is for sure!

Answer 4

didn't understand amestri exactly

Answer 5

so a limit is like asking "what value is the function approaching as the input approaches this number?"

Answer 6

I don't know but I would say -3 cause probably number approaching -1 would be irrational I don't know

Answer 7

so if you have something like y=5x, then the limit as x-->5 of the function y is 25.

Answer 8

because no matter what you pick for your epsilon, there will be both rational and irrational numbers in the interval \[(1-\epsilon,1+\epsilon)\]

Answer 9

DNE is incorrect - teacher just said so

Answer 10

a limit doesn't exist when the two sides of the function don't approach the same output for the input point/

Answer 11

oh crap we are all wrong! ho ho ho ho

Answer 12

oops! i'm sorry, here the limit exists...this is because , around the point both of them give the same limit of -3.

Answer 13

wasn't paying attention as usual. limit is -3

Answer 14

lol

Answer 15

same case as sat! :)

Answer 16

cause there is no x where it says irrational?

Answer 17

as x goes to 1 through rationals limit is -3
as x goes to 1 through irrational limit is also -3 because the function is identically -3 there. so limit is surely -3

Answer 18

concept:
when x converges to a point say a, u hav both rational and irrational values around it...u say limit for a function exists only if , the functional value converges to a single point(here -3).but wen a function is such that it takes different values for rational no. and irrational no., the functional value oscillates between the 2. therefore genarally limit doesnot exist. but in this problem , there's no case, of oscillation and hence limit exists.
PS:slowly read through this,if u hav doubts post it.