How can you show the working for limits as t approaches infinity?

[nokia8650]

eg. y = 5ke^(-0.2t) - 5k + 2

How would one show the working to show what happens as t tends to infinity? Would something like this be ok?

as t--> infinity

e^(-0.2t) --> 0

therefore 5ke^(-0.2t) ---> 0

therefore 5ke^(-0.2t) - 5k + 2 --> 5k + 2

therefore y ---> 5k + 2

Thanks

 

[Defennder]

Looks ok. But you left out a minus sign.

 

[tiny-tim]

How would one show the working …

Hi nokia8650!

I guess it means a delta-epsilon proof.

 

[HallsofIvy]

No, I would not say that "show the working" means a "delta- epsilon" proof. What You have done is correct. You might add something like "Since f(x)= e^x increases without bound as x increases, e^(-0.2t) --> 0 as t --> infinity".