DiffIntReview

DiffIntReview - Math 1042 Differentiation and...

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Unformatted text preview: Math 1042 Differentiation and Antidifferentiation Review Problems In Problems 1–15, calculate y . Simplify your answers when possible. 1. y = (x4 − 3x2 + 5) 4. y = t 1 − t2 5 2. y = cos3 (πt) 5. y = esin(2θ) √ 8. y = tan( 1 − x) 11. y = x tan−1 (4x) 3. y = 1 x+ √ 3 x4 6. y = sin−1 (ex ) 9. y = ln (x2 ex ) √ 7. y = x3 e−1/x 10. y = sec (1 + x2 ) 13. y = ln (ln x) 12. y = cot (3x2 + 5) In Problems 16–23, find the indefinite integral (the most general antiderivative). 14. x3 − 1 x3 dx 15. √ 3 1 x+ √ 3 x 5 x dx dx 16. πx π cos dx 2 2 (2ex − 3e−2x ) dx 17. (4 sec θ tan θ − 2 sec2 θ) dθ 1 dx + 1) 18. 1− 19. 20. 2(x2 Solve the initial value problems. 21. f (x) = √ x (6 + 5x), f (1) = 10 2 , x < 0; f (−1) = 7 x 22. f (x) = 2x + 23. f (t) = sin t + cos t, f (π ) = 3 ...
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This note was uploaded on 04/19/2011 for the course MATH 1042 taught by Professor Dr.z during the Spring '08 term at Temple.

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