Basic Analysis I — Real Analysis · Problem 6.1.2

Sequences of Functions — Jiri Lebl

Mathematics — Real Analysis · pointwise-and-uniform-convergence

Problem

(a)) Find the pointwise limit

\dfrac{e^{x/n}}{n}

for

x \in \mathbb{R}

. (b)) Is the limit uniform on

\mathbb{R}

? (c)) Is the limit uniform on

[0, 1]