10. Sequences of Functions

Pointwise Convergence — Quiz

Test your understanding of pointwise convergence with 5 practice questions.

Practice Questions

Question 1

Which statement best describes pointwise convergence of a sequence of functions $f_n$ to a function $f$ on a set $D$?

Question 2

What is the pointwise limit of $f_n(x)=\frac{x}{n}$ on $\mathbb{R}$?

Question 3

What is the pointwise limit of $f_n(x)=x^n$ on $[0,1]$?

Question 4

Let $f_n(x)=\sin\left(\frac{x}{n}\right)$ on $\mathbb{R}$. What is the pointwise limit function?

Question 5

Suppose $f_n(x)=c_n$ for every $x$ in a domain $D$, where $c_n\to c$ as $n\to\infty$. What is the pointwise limit of $f_n$ on $D$?