The following r(t) = (3 sint, 4 cost) represents vector-valued function. i) ii) iii) By eliminating parameter t, show that its rectangular equation can be written 9 16 Ans: = 1. Find rand r I r'(t) = (3 cost,-4 sint) • (#) - (³1/², 2√²). * (=)- (³1/2² -2 √²) 3√2 2 4 Sketch the parametric curve with its orientation and indicate the position vec

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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The following
r(t)=(3 sint, 4 cost)
represents vector-valued function.
i)
ii)
iii)
By eliminating parameter t, show that its rectangular equation can be written as
x² v²
+
9 16
Find r
dr (7)
Ans:
= 1.
and r' =
r' (t) = (3 cost,-4 sint)
• (²7) - (³1/²,2 √²). ~ (=) - (¹1/²₁-2₂√²)
Sketch the parametric curve with its orientation and indicate the position vector
and tangent vector at t =
π
4
based on the answer in ii).
Transcribed Image Text:The following r(t)=(3 sint, 4 cost) represents vector-valued function. i) ii) iii) By eliminating parameter t, show that its rectangular equation can be written as x² v² + 9 16 Find r dr (7) Ans: = 1. and r' = r' (t) = (3 cost,-4 sint) • (²7) - (³1/²,2 √²). ~ (=) - (¹1/²₁-2₂√²) Sketch the parametric curve with its orientation and indicate the position vector and tangent vector at t = π 4 based on the answer in ii).
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