H be the set of all points (x, y) in ℝ2 such that x2 + xy 3y2 = 3. Show that H is a closed subset of ℝ2 (considered with the Euclidean metric). Is H bounded?

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Q: Question 1) The dimension of the subspace of P3 consisting of all vectors of the form at³ +bt² + ct…

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Q: If A and B are square matrices of the same order such that AB=BA, then prove by induction that AB" =…

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Q: (D² − 1)y=e*(x² + 1)

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Q: ²+ b² + c²p²-2(ab + bc+c

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Q: { ∞ ^ > ㅣ 8. Determin S 9"+5 S

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Q: For each of the following series, determine whether the series converges, diverges to ±∞, or…

A: We have been given the following series: i. ∑n=1∞sin23n+22n2-3 ii. ∑n=1∞1n-2π iii. ∑n=1∞n+1n3+2 We…

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Q: 2. Determine half range Fourier sine series for f(x)=x(n-x) in 0<x< T hence deduce +3/3+²/2+ π³/3².

A: Since you haveposted multiple questions, we will solve the first question for you. If you want any…

Q: 1) The dimension of the subspace of P3 consisting of all vectors of the form at³+bt2 + ct+d, where b…

A: We have to find the dimension of the subspace of P3 which consists the vector at3+bt2+ct+d   where…

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Q: Evaluate I = f(sin x +9y) dx + (8x + y) dy for the nonclosed path ABCD in the figure. I = D A с B A…

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Q: Find and classify the critical points of z(x, y) = x³ + 5x² + 5x + y² - 2xy.

A: Given: z=fx, y=x3+5x2+5x+y2-2xy To find: Critical points and classify them.