# Proofs of limit properties

Watch
Announcements
#1
Hi when you are proving properties about limits of functions i.e the sum rule, the product rule and so on do you have to do seperate proofs for when.

the limits are at a finite point and when they are at infinity, but real valued?

Also when the limits are infintely valued do you need seperate proofs to show the properties in this case.

thanks
0
1 year ago
#2
Can you give an example?
(Original post by robbothedon)
Hi when you are proving properties about limits of functions i.e the sum rule, the product rule and so on do you have to do seperate proofs for when.

the limits are at a finite point and when they are at infinity, but real valued?

Also when the limits are infintely valued do you need seperate proofs to show the properties in this case.

thanks
0
#3
(Original post by mqb2766)
Can you give an example?
so say f(x)->l as x->a and g(x)->p as x->a then the sum rule in this case would be involving real value limits at finite points.

f(x)+g(x) -> l + p as x-.a

So you could prove this if you wanted. This is the property given in begginers analysis books. But when i compute limits often i will be computing limits at infinity and limits which have infinite values. When i am computing limits at infinity but the limits involved have real values the sum rule above works.

say f(x)-> l as x-> infinity and g(x)->p as x-> infinity then

f(x)+g(x) -> l + p as x goes to infinity.

Now when you compute the limit you are really using the second property here i believe. Would this property require a seperate proof. thanks
0
1 year ago
#4
Strictly speaking you need different proofs for the +/-infinity cases. But the proofs are similar enough that people often don't worry about it.
0
#5
(Original post by DFranklin)
Strictly speaking you need different proofs for the +/-infinity cases. But the proofs are similar enough that people often don't worry about it.
Ah thank you
0
1 year ago
#6
(Original post by robbothedon)
so say f(x)->l as x->a and g(x)->p as x->a then the sum rule in this case would be involving real value limits at finite points.

f(x)+g(x) -> l + p as x-.a

So you could prove this if you wanted. This is the property given in begginers analysis books. But when i compute limits often i will be computing limits at infinity and limits which have infinite values. When i am computing limits at infinity but the limits involved have real values the sum rule above works.

say f(x)-> l as x-> infinity and g(x)->p as x-> infinity then

f(x)+g(x) -> l + p as x goes to infinity.

Now when you compute the limit you are really using the second property here i believe. Would this property require a seperate proof. thanks
You would need separate proofs for limit at a finite value and infinite value because the definition of the limit is slightly different.
0
X

new posts
Back
to top
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

### Poll

Join the discussion

#### Have you experienced financial difficulties as a student due to Covid-19?

Yes, I have really struggled financially (44)
18.11%
I have experienced some financial difficulties (68)
27.98%
I haven't experienced any financial difficulties and things have stayed the same (92)
37.86%
I have had better financial opportunities as a result of the pandemic (30)
12.35%
3.7%