Basic Analysis I — Real Analysis · Problem 3.1.1

Continuous Functions — Jiri Lebl

Mathematics — Real Analysis · limits-of-functions

Problem

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

\lim_{x \to c} \sqrt{x}

, for

c \geq 0

\lim_{x \to c} x^2 + x + 1

, for

c \in \mathbb{R}

\lim_{x \to 0} x^2 \cos(1/x)

\lim_{x \to 0} \sin(1/x)\cos(1/x)

\lim_{x \to 0} \sin(x)\cos(1/x)