Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Analysis Uniform Convergence
Let fn : [0, 1] → ℝ be given by
fn(t) = (n + 2) ( n+ 1)tn (1 - t), for all t in [0, 1].
Which of the following is true?
1
The sequence (fn) converges uniformly.
2
The sequence (fn) converges pointwise but not uniformly.
3
he sequence (fn) diverges on [0, 1).
4
\(\displaystyle\lim _{n \rightarrow \infty} \int_0^1 f_n(t) d t\) = \(\displaystyle \int_0^1 \lim _{n \rightarrow \infty} f_n(t) d t \).
5
Question Not Attempted