IITM BS Question 6 - Week 9 Practice

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IITM BS Question 6 - Week 9 Practice | Prasnya

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Q6Comprehension7 Marks10 May 2026

Passage

Consider the function

f: \mathbb{R}^3 \to \mathbb{R}

defined as

f(x, y, z) = e^{x^2 + y^2 + z^2}

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

Suppose the function f describes the pressure in a room at point

(x, y, z)

\mathbb{R}^3

. If the rate of change of pressure at

(-1, -1, 1)

in the direction of the unit vector 1/sqrt(3)

(1, 1, 1)

is k * e^3. Find k up to two decimal points.

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10 May 2026

Mathematics 2 · Week 9

Q6.Suppose the function f describes the pressure in a room at point

(x, y, z)

\mathbb{R}^3

. If the rate of change of pressure at

(-1, -1, 1)

in the direction of the unit vector 1/sqrt(3)

(1, 1, 1)

is k * e^3. Find k up to two decimal points.@passage

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