IITM BS Question 10 - Week 10 Practice

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IITM BS Question 10 - Week 10 Practice | Prasnya

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Q10Comprehension5 Marks21 Dec 2025

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Based on the above data, answer the given subquestions. Consider the function

f: \mathbb{R}^2 \to \mathbb{R}

defined by

f(x, y) = x^2 + y^2 + xy + 3x + 1

, for all

(x, y) \in \mathbb{R}^2

Consider the sequence of points x_n= (-2 + 1/n, 1 + 1/n) for n in {1, 2, }. The tangent hyperplane to the graph of f at x_n has a unique normal of the form (x_n, x_n, -1). Find lim_{n -> infinity} x_n+ lim_{n -> infinity} x_n.

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Q10

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21 Dec 2025

Mathematics 2 · Week 10

Q10.Consider the sequence of points x_n= (-2 + 1/n, 1 + 1/n) for n in {1, 2, }. The tangent hyperplane to the graph of f at x_n has a unique normal of the form (x_n, x_n, -1). Find lim_{n -> infinity} x_n+ lim_{n -> infinity} x_n.@passage

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