10. Sequences of Functions

Uniform Convergence — Quiz

Test your understanding of uniform convergence with 5 practice questions.

Practice Questions

Question 1

Which statement is equivalent to uniform convergence of $f_n$ to $f$ on a set $A$?

Question 2

For $f_n(x)=\frac{x}{n}$ on $[0,1]$, what is $\sup_{x\in[0,1]}|f_n(x)-0|$?

Question 3

Does $f_n(x)=x^n$ on $[0,1]$ converge uniformly to its pointwise limit?

Question 4

If each $f_n$ is continuous on an interval $I$ and $f_n\to f$ uniformly on $I$, what can be concluded about $f$?

Question 5

Which statement is always true if $f_n\to f$ uniformly on a set $A$?