Anonymous
Anonymous asked in 科學數學 · 1 decade ago

微積分解題!!

3.Determine the set of points at which the function is continuous.

(a) F(X)=sin(xy)/e的x次方-y平方 (b) G(x)=ln (x的平方+y的平方-4)

2 Answers

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  • 1 decade ago
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    (a)sin(xy)is continuous on all points of (x,y)屬於R2ex-y2 is also continuous on all points of (x,y)屬於R2Hence (sin(xy))/(ex-y2) is also continuous on (x,y)屬於R2but sin(xy)/(ex-y2) is not defined on ex=y2so the set of points which sin(xy)/ex-y2 is continuous are{(x,y)屬於R2|ex≠y2}(b)G(x)=ln(x2+y2-4)is continuous at (x,y)屬於R2,but x2+y2 must be not equal to 4Hencs G(x,y)=ln(x2+y2-4)is continuous at all points{(x,y)屬於R2|x2+y2≠4}

    Source(s): me
  • 1 decade ago

    我想你的函數應該是指

    (a)F(x,y)=sin(xy)/(e^x-y^2)

    F(x,y) is continuous at {(x,y) belong to R2:e^x not equal to y^2}

    (b)G(x,y)=ln(x^2+y^2-4)

    G(x,y) is continuous at {(x,y) belong to R2:x^2+y^2-4 not equal to 0}

    that is {(x,y) belong to R2:dist((x,y),(0,0)) not equal to 2}

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