Lebl-Basic-Analysis-I · Problem 3.1.1

Continuous Functions

Mathematics · limits-of-functions

Problem

Find the limit (and prove it of course) or prove that the limit does not exist

\begin{aligned} &\text{a) } \lim_{x \to c} \sqrt{x}, \text{ for } c \geq 0 \qquad \text{b) } \lim_{x \to c} x^2 + x + 1, \text{ for } c \in \mathbb{R} \qquad \text{c) } \lim_{x \to 0} x^2 \cos(1/x)\\ &\text{d) } \lim_{x \to 0} \sin(1/x)\cos(1/x) \qquad \text{e) } \lim_{x \to 0} \sin(x)\cos(1/x) \end{aligned}