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UCB - MCD4500 Engineering Mathematics - Trimester 2 - 2025

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If what is/are the local maximum value/values of  f. Only write the number/numbers separating by "," . If there is no maximum value answer "no"

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Consider the function .  What is the directional derivative at the point in the direction ?

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Let . Then at the point , compute  

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Let . Compute .

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grad (f) is a vector.

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 Directional derivative is a vector.

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The angle between the planes and is where is equal to  

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Let

be the plane passing through the points

,

, and

.

Where does the line

intersect this plane?

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Write down a normal vector to the plane .

Write the answer in < > form

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Write down an equation for the plane passing through the points

,

, and

.

Express your answer in the form

where

, , ,

are positive integers with no common factor.

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