IITM BS Question 12 - Week 10 Practice

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IITM BS Question 12 - Week 10 Practice | Prasnya

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Q12Comprehension5 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) = \frac{1}{1 + x^2 + y^2}

, for all

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

Consider the sequence of points x_n= (1/n, 1/n) for n in {1, 2, }. The tangent plane to the graph of f at x_n has a unique normal x_nof the form (x_n, x_n, -1). If theta_n denotes the angle (in degrees) between x_n and the vector

(0, 0, -1)

, then find the value of lim_{n -> infinity} theta_n.

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Q12

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21 Dec 2025

Mathematics 2 · Week 10

Q12.Consider the sequence of points x_n= (1/n, 1/n) for n in {1, 2, }. The tangent plane to the graph of f at x_n has a unique normal x_nof the form (x_n, x_n, -1). If theta_n denotes the angle (in degrees) between x_n and the vector

(0, 0, -1)

, then find the value of lim_{n -> infinity} theta_n.@passage

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