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4. Let y: R – R³ be given by r(t) = (a cos(wt), a sin(wt), but). for some nonzero a, b, w. (i) Show that Y(t)| is constant. (ii) Show that y'(t) forms a constant nonzero angle with the z axis. (iii) Let ti = 0 and t2 = 2. Prove that y(t2) – 7(t1) # (t2 – t1)Y(7) for any TE (t1, t2). (This shows the failure of the Mean Value Theorem for vector-valued functions!)

4. Let y: R – R³ be given by r(t) = (a cos(wt), a sin(wt), but). for some nonzero a, b, w. (i) Show that Y(t)| is constant. (ii) Show that y'(t) forms a constant nonzero angle with the z axis. (iii) Let ti = 0 and t2 = 2. Prove that y(t2) – 7(t1) # (t2 – t1)Y(7) for any TE (t1, t2). (This shows the failure of the Mean Value Theorem for vector-valued functions!)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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4. Let y : R → R³ be given by y(t) = (a cos(wt), a sin(wt), but). for some nonzero a, b, w. (i) Show that Y(t)| is constant. (ii) Show that y'(t) forms a constant nonzero angle with the z axis. (iii) Let ti = 0 and t2 = 2. Prove that (t2) – y(tı) # (t2 – t1)Y(7) for any T E (t1, t2). (This shows the failure of the Mean Value Theorem for vector-valued functions!)
Transcribed Image Text:4. Let y : R → R³ be given by y(t) = (a cos(wt), a sin(wt), but). for some nonzero a, b, w. (i) Show that Y(t)| is constant. (ii) Show that y'(t) forms a constant nonzero angle with the z axis. (iii) Let ti = 0 and t2 = 2. Prove that (t2) – y(tı) # (t2 – t1)Y(7) for any T E (t1, t2). (This shows the failure of the Mean Value Theorem for vector-valued functions!)
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