By I. N. Herstein
New version contains vast revisions of the fabric on finite teams and Galois thought. New difficulties additional all through.
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New version contains wide revisions of the fabric on finite teams and Galois concept. New difficulties additional all through.
Additional resources for Topics in Algebra, Second Edition
T16. Name the concept of calculus that means instantaneous rate of change. T17. You can estimate derivatives numerically from tables of data. Estimate f (4) (read “f -prime of four”), the derivative of f ( x ) at x = 4. 7 24 29 31 35 42 T18. What did you learn from this test that you did not know before? 29 Properties of Limits Finding the average velocity of a moving vehicle requires dividing the distance it travels by the time it takes to go that distance. You can calculate the instantaneous velocity by taking the limit of the average velocity as the time interval approaches zero.
For Problems 3–12, state whether the function has a limit as x approaches c; if so, tell what the limit equals. Q7. What graphical method can you use to estimate the value of a definite integral? Q8. Write the graphical meaning of derivative. Q9. Write the physical meaning of derivative. 3. 4. Q10. If log 3 x = y, then A. 3 x = y D. y3 = x Section 2-2: B. 3 y = x E. xy = 3 C. x3 = y Graphical and Algebraic Approaches to the Definition of Limit © 2005 Key Curriculum Press 37 6. 5. 7. 15. 7 16. 8 17.
D. Use your trapezoidal rule program to estimate the integral using 50 increments and 100 increments. How close do T50 and T100 come to 15, the exact value of the integral? Do the trapezoidal sums seem to be getting closer to 15 as the number of increments increases? Which concept of calculus is used to determine this? R5. In Section 1-5, you started a calculus journal. In what ways do you think keeping this journal will help you? How can you use the completed journal at the end of the course? What is your responsibility throughout the coming year to ensure that keeping the journal will be a worthwhile project?
Topics in Algebra, Second Edition by I. N. Herstein