Pre-Calc Homework Solutions 242

Pre-Calc Homework Solutions 242 - 242 dy dx Section 6.2 1...

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Unformatted text preview: 242 dy dx Section 6.2 1 (sec x tan x sec x tan x sec x tan x sec2 x sec x tan x sec x(tan x sec x) sec x tan x 9. sec2 x) 4. u du 7x 7 dx 2 1 du 7 dx 2)3 dx 1 28u3 du 7 28(7x u4 C 2)3(7) (7x 2)4 C 2)3 sec x 10. dy dx 1 ( csc x cot x csc x cot x csc x cot x csc2 x csc x cot x csc x(cot x csc x) csc x cot x d Check: [(7x dx 2)4 C] 4(7x 28(7x csc2 x) 5. u du 3 du x 3 1 dx 3 dx 3u 9 9u 2 csc x x2 dx Section 6.2 Exercises 1. u du 1 du 3 3x 3 dx dx 1 sin u du 3 1 cos u C 3 1 cos 3x C 3 1 cos 3x 3 sin 3x dx 9 du 3 9 u2 1 1 du 3 u2 1 1 tan 1 u C 3 1 x tan 1 C 3 3 d 1 x Check: tan 1 C dx 3 3 1 3 1 1 x 2 3 1 3 1 9 x2 d Check: dx C 1 ( sin 3x)(3) 3 6. u sin 3x du 1 r3 3r 2 dr 2. u du x dx 2x 2 4x dx 1 du 4 1 du r 2 dr 3 9r2 dr 1 r 3 9 1 3 du u 1/2 3 u du C r3 C C) 9r 2 1 r3 1 cos u du 4 1 sin u C 4 1 sin (2x 2) C 4 1 d 1 Check: sin (2x 2) C cos (2x 2)(4x) 4 dx 4 x cos (2x 2) dx 3(2)u1/2 6 1 Check: x cos (2x2) d ( 6 dx 1 r3 6 1 2 1 r3 ( 3r 2) 3. u du 2x 2 dx dx 1 sec u tan u du 2 1 sec u C 2 1 sec 2x C 2 1 C sec 2x tan 2x 2 7. u du 1 cos t 2 1 du 2 sec 2x tan 2x dx 1 t sin dt 2 2 t 2 du sin dt 2 t 2 t 1 cos sin dt 2 2 2 u2 du 2 3 u 3 2 1 3 C cos t 3 2 Check: 2x d 1 sec 2x dx 2 C 2 sec 2x tan Check: d 2 1 cos dx 3 2 t 2 t 1 2 1 cos sin 2 2 2 2 t t 1 cos sin 2 2 t 3 C ...
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.

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