Exercise 77Calculus › Multivariable calculus › ContinuityHigh schoolAdded 3 Nov 2026

Continuity of a rational function

#rational function#domain#continuity

Statement

Where is $f(x,y)=\dfrac{x+2y}{x^2+y^2+1}$ continuous?

Hint

A quotient of continuous functions is continuous wherever the denominator is nonzero.

Show solutionHide solution

Denominator. $x^2+y^2+1\neq0$ for every $(x,y) \in \mathbb{R}^2$ .

Continuity. $f$ is continuous on $\mathbb{R}^2$ .