Exercise 225Calculus › Multivariable calculus › ContinuityHigh schoolAdded 3 Nov 2026

Continuity of a polynomial

#continuity#polynomial#continuity everywhere

Statement

Show that $f(x,y)=x^2+3xy-y^2+2x-1$ is continuous on $\mathbb{R}^2$ .

Hint

Polynomials in several variables are continuous (sums and products of continuous coordinate projections).

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Solution

Continuity of polynomials. The functions $(x,y)\mapsto x$ and $(x,y)\mapsto y$ are continuous, and sums/products of continuous functions are continuous.

Conclusion. $f$ is continuous on $\mathbb{R}^2$ by the composition rules.

Continuity of a polynomial

Statement

Solution

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