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Find the Length of the Curve r(t)=2titj+tk,2t1\mathbf { r } ( t ) = - 2 t \mathbf { i } - t \mathbf { j } + t \mathbf { k } , - 2 \leq t \leq 1

question 11

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Find the length of the curve r(t) =2titj+tk,2t1\mathbf { r } ( t ) = - 2 t \mathbf { i } - t \mathbf { j } + t \mathbf { k } , - 2 \leq t \leq 1 .


Definitions:

KMnO4

Potassium permanganate, a strong oxidizing agent used in various chemical reactions, including organic synthesis and analytical chemistry.

Na2Cr2O7

Sodium dichromate is an inorganic compound consisting of sodium, chromium, and oxygen, used as an oxidizing agent in various chemical reactions, including those in organic chemistry.

Fatty Acid

A type of carboxylic acid that is often found in lipids, characterized by a long hydrocarbon chain which can be saturated or unsaturated.

Wax

A class of chemical compounds that are malleable at ambient temperatures and typically melt upon heating, often of natural or synthetic origin.

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