Similarities and differences between function limit and sequence limit

Several approaching forms of function limit: X tends to positive infinity; X tends to negative infinity; X tends to infinity; X left approaches x0; X right approaches x0; X tends to be close to x0. And it increases continuously. The limit of sequence is only that n tends to positive infinity, and it is a discrete increase. Formally, sequence is a function

What is the difference between function limit and sequence limit?

The sequence can be expressed as a function
The limit of sequence is the limit of function

What functions are not integrable except those defined in open intervals and unbounded functions?

Dirichlet function, defined as follows:
When d (x) = 1, X is a rational number
When d (x) = 0 and X is an irrational number

On the proof method of sequence limit If n -- > ∞ is proved, [sqrt (n ^ 2 + A ^ 2)] / N -- > 1, Can the sequence x [n] = [sqrt (n ^ 2 + A ^ 2)] / n be enlarged into | A / N |? The standard answer is: A ^ 2 / N * [1 / ((sqrt (n ^ 2 + A ^ 2) + n)]

Sequence x [n] = [sqrt (n ^ 2 + A ^ 2)] / n

Proof of sequence limit How to prove LIM ((n + 2) / (n ^ 2-2)) sin n = 0

lim(n+2)/(n^2-2)=lim(1/n+2/n^2)/(1-2/n^2)=0.
Also ((n + 2) / (n ^ 2-2)) sin n|

On the proof of sequence limit Let {xn} of a special sequence be a nonnegative real sequence. It satisfies XM + n

According to XM + N0, n \ xn is bounded
Then xn / N when n tends to infinity, the limit exists
What you said downstairs
Xn = 1 / N does not converge; but
Xn / N = 1 / N ^ 2 is a convergent series

Similarities and differences between function limit and sequence limit