Find the Length of the Curve $\mathbf { r } ( t ) = - 2 t \mathbf { i } - t \mathbf { j } + t \mathbf { k }$

question 46

Multiple Choice

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

• A) \(3 \sqrt { 6 }\)
• B) \(\sqrt { 6 }\)
• C) \(2 \sqrt { 6 }\)
• D) \(6 \sqrt { 6 }\)

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Definitions:

Par Value

Par value is the face value of a bond or stock as stated by the issuing company, which may differ from its market value; for stocks, it is often a nominal amount.

Coupon

The interest rate stated on a bond when issued, which is paid by the issuer to the bondholder at specified intervals until maturity.

Yield To Maturity

The total return anticipated on a bond if it is held until it matures, considering both interest payments and capital gains.

Real Rate

The expected return rate an investor anticipates, adjusted for inflation.