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f(t) = (cost, Sint, t) f'(t) = (-sint, west, 1) 1 f'(x)) = √√(-sint) ² + ((ost ) ² + 12 F(t)= - √Sin't+st+1 =√1+1 = √₂ - f(t) [f'(+)) (-Sint, lost, 1) ) = (t) y N²t) Ĵ 1. 25 - last -Sint 1 lost -Sint 1 = 1 (0+ sind)-3 (0+ Cat ) +R (= sint + cost) = Sintî - ustî + 2 k .. B (t) = (sint, - Lost, 1/2) = [( sint, - lest, Now, f"lt) = (- Cost, -sint, 0) ^ ^

f(t) = (cost, Sint, t) f'(t) = (-sint, west, 1) 1 f'(x)) = √√(-sint) ² + ((ost ) ² + 12 F(t)= - √Sin't+st+1 =√1+1 = √₂ - f(t) [f'(+)) (-Sint, lost, 1) ) = (t) y N²t) Ĵ 1. 25 - last -Sint 1 lost -Sint 1 = 1 (0+ sind)-3 (0+ Cat ) +R (= sint + cost) = Sintî - ustî + 2 k .. B (t) = (sint, - Lost, 1/2) = [( sint, - lest, Now, f"lt) = (- Cost, -sint, 0) ^ ^

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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11. f(t) = (cost, Sint, t) f'(t) = (-sint, lost, 1) 1 f'(t)) = √√(-sint) ² + (6074 ) ² + /2 .:: F(t)= = √ Sin't + Lost +1 ... Ñ(t) = = = [1 = 1+1 = √₂ 2 ll fét) [f'(+)) (-sint, cost, 1) √2 √₂ T'lt) = = // ( - Cost₁ - Sint, o) [ -= '( + ) ) = √ ( + ) ^ ( - lost ) ² + (-sint) " +0³) (-Sint, Lost, 1 ( // 2₂2 √ √ 4₁²++ sin²+ +0 1 V₂ VT 늠 71(f) 17'(+)1 +2 (-ost, -sint,0) 1 $22 -=[(- list, -sint, 0) B(x) = F(t) x N²t) î Ĵ Sint & lost √2 - lost -Sint гу K = ₁ (0+ sint)- ³² (0+ (at) + ^ ( = /2 sint + √2 cost) Lost ƒ' (t) x {"(t) = = Sinti - cost ↑ + = /2₂2 î .. Blt) = |( sint, - Lost, + / 2 ) .: Kt) = 1 Now, f"lt) = (- cost, -sint, 0) 2 الله -Sint - Lost (.r Lost -Sint <d = √1+1 = √2 √₂ metop 11. f ( t ) x + ( + ) 11 11 f' (t)11 3 1 O = ² (0+ sint) -Ĵª (0+ cast) +k (bint+(ast) = Sinti - cost î+ k 2 · || f'(t)x f"(t)|| = √ sin³+ + (-uost)^² +1² = √ Sir²³t+cos³²7 +1 √2 3 (√2)³ (1 N/A
Transcribed Image Text:11. f(t) = (cost, Sint, t) f'(t) = (-sint, lost, 1) 1 f'(t)) = √√(-sint) ² + (6074 ) ² + /2 .:: F(t)= = √ Sin't + Lost +1 ... Ñ(t) = = = [1 = 1+1 = √₂ 2 ll fét) [f'(+)) (-sint, cost, 1) √2 √₂ T'lt) = = // ( - Cost₁ - Sint, o) [ -= '( + ) ) = √ ( + ) ^ ( - lost ) ² + (-sint) " +0³) (-Sint, Lost, 1 ( // 2₂2 √ √ 4₁²++ sin²+ +0 1 V₂ VT 늠 71(f) 17'(+)1 +2 (-ost, -sint,0) 1 $22 -=[(- list, -sint, 0) B(x) = F(t) x N²t) î Ĵ Sint & lost √2 - lost -Sint гу K = ₁ (0+ sint)- ³² (0+ (at) + ^ ( = /2 sint + √2 cost) Lost ƒ' (t) x {"(t) = = Sinti - cost ↑ + = /2₂2 î .. Blt) = |( sint, - Lost, + / 2 ) .: Kt) = 1 Now, f"lt) = (- cost, -sint, 0) 2 الله -Sint - Lost (.r Lost -Sint <d = √1+1 = √2 √₂ metop 11. f ( t ) x + ( + ) 11 11 f' (t)11 3 1 O = ² (0+ sint) -Ĵª (0+ cast) +k (bint+(ast) = Sinti - cost î+ k 2 · || f'(t)x f"(t)|| = √ sin³+ + (-uost)^² +1² = √ Sir²³t+cos³²7 +1 √2 3 (√2)³ (1 N/A
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