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Exercise 9. Use the above formula, together with definition of T, to show that Va(t)||°||a"(t)||² – (a'(t), a"(t))² ||a'(t)||3 K(t :

Exercise 9. Use the above formula, together with definition of T, to show that Va(t)||°||a"(t)||² – (a'(t), a"(t))² ||a'(t)||3 K(t :

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.4: Derivatives Of Exponential Functions
Problem 2E
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Exercise 9
Exercise 9. Use the above formula, together with definition of T, to show that Vla'(t)||°||a"(t)||? – (a'(t), a"(t)}² ||a'(t)|| 3 K(t) = In particular, in R³, we have ||a'(t) x a"(t)|| |la'(t)||3 K(t) = (Hint: The first identity follows from a straight forward computation. The second identity is an immediate result of the first via the identity ||v x w||² = |||||° – (v, w)².)
Transcribed Image Text:Exercise 9. Use the above formula, together with definition of T, to show that Vla'(t)||°||a"(t)||? – (a'(t), a"(t)}² ||a'(t)|| 3 K(t) = In particular, in R³, we have ||a'(t) x a"(t)|| |la'(t)||3 K(t) = (Hint: The first identity follows from a straight forward computation. The second identity is an immediate result of the first via the identity ||v x w||² = |||||° – (v, w)².)
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