Question

Is the following statement "Let ( f(x, y)=left{egin{array}{ll}frac{x^{2}-2 x y}{x^{2}-4 y^{2}} & ext { if }(x, y) eq(2,1) \ frac{1}{2} & ext { if }(x, y)=(2,1)end{array} ight. ). Then ( f(x, y) ) is continuous at the point ( (2,1) ) " true or false?

          Is the following statement
"Let ( f(x, y)=left{egin{array}{ll}frac{x^{2}-2 x y}{x^{2}-4 y^{2}} & 	ext { if }(x, y) 
eq(2,1) \ frac{1}{2} & 	ext { if }(x, y)=(2,1)end{array}
ight. ). Then ( f(x, y) ) is continuous at the point ( (2,1) ) " true or false?

$Is the following statement "Let ( f(x, y)=lefteginarrayllfracx^2-2 x yx^2-4 y^2 ext if (x, y) eq(2,1) frac12 ext if (x, y)=(2,1)endarray ight. ). Then ( f(x, y) ) is continuous at the point ( (2,1) ) " true or false?$

Added by Saadet Burcu T.

Calculus, Early Transcendentals

Michael Sullivan, Kathleen Miranda 1st Edition

Chapter 1

Instant Answer

Solved by Expert Luis Garcia

06/06/2023

Step 1

If the limit exists and is equal to the value of the function at (2, 1), then the function is continuous at that point. Let's find the limit: $\lim_{(x, y) \to (2, 1)} \frac{x^2 - 2xy}{x^2 - 4y^2}$ Show more…

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