By Jerrold Marsden, Alan Weinstein
Undergraduate Texts in arithmetic
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Extra info for Calculus I (Undergraduate Texts in Mathematics)
8. How can we be sure not to have missed still more bumps and wiggles? By plotting many points we can Some hints for carrying out these calculations on your calculator are contained in the Student Guide. Copyright 1985 Springer-Verlag. All rights reserved. 44 Chapter R Review of Fundamentals make good guesses but can never know for sure. The calculus we will develop in Chapters 1 to 3 of this book can tell us exactly how many wiggles the graph of a function can have and so will greatly facilitate plotting.
12. 13. 14. 15. 16. 8x+2>0 lox-6<5 x2-5<0 x 2 - 5x 6 < 0 x 2 - ( X - 1)'>2 x3> 1 3x2- 7 < 0 x 2 - 2x 1 > 0 + + Copyright 1985 Springer-Verlag. All rights reserved. Review Exercises for Chapter R Describe in terms of intervals the set of x satisfying the conditions in Exercises 17-24. 17. x2 < 1 18. IX - 11 < 2 19. x2 - 2x < 0 20. 8x - 3 > 0 21. Ix - 112 > 2 22. x 2 - 7x 12 > 0 23. x 2 - l l x + 3 0 < 0 24. Ix - 31 < 2 Find the x satisfying the conditions of Exercises 25-28. 25. x < 10 and x3 E ( - 8,27) 26.
C)3years? (d)20years? 2=4. (b) In 18 = 6 + 6 + 6 years it increases by a factor 2 . 2 . 2 = 8. (c) In 3 years, let it increase by a factor k. Then in 6 years we get k . 4142. 0794. 3 Simplify the expressions in Exercises 1-20. 13. 25/3/47/3 14. 3-8/"(1/9)-4/11 15. 1 2 ~ 1182/3 ~ 16. 207/~. 5-7/2 17. (x3/2 + x5/2)x -3/2 18. ( ~ ~ 1 ~ ) " ~ 19. ~ ~ / ~ ( +x2 x- 1~i 2+ / 3x7l2) ~ + 20. y"2(1/y 2 G +y-1/3) Using the laws of rational exponents, verify the root formulas in Exercises 21 and 22. * a 22.
Calculus I (Undergraduate Texts in Mathematics) by Jerrold Marsden, Alan Weinstein