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MAT 1221 Survey of Calculus

MAT 1221 Survey of Calculus. Exam 1 Info. http://myhome.spu.edu/lauw. Expectations. (Time = 15 min.) Use equal signs correctly Use and notations correctly Pay attention to the independent variables: Is it or ?. Tutoring Bonus Points. Turn in your paper today!

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MAT 1221 Survey of Calculus

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  1. MAT 1221Survey of Calculus Exam 1 Info http://myhome.spu.edu/lauw

  2. Expectations • (Time = 15 min.) • Use equal signs correctly • Use and notations correctly • Pay attention to the independent variables: Is it or ?

  3. Tutoring Bonus Points • Turn in your paper today! • Get the new paper for the next exam!

  4. Exam 1 • Date and Time: 4/24 Thursday (5:30-6:50 pm) • Section 1.5, 2.1-2.5, B.1, B.2 • Total Points: 80 points

  5. Exam 1 • This exam is extremely important. • The second exam is on 5/15. The last day to withdraw is 5/9. So this exam gives us the critical info for you to make a sound decision.

  6. Calculators • Absolutely no share of calculators. Bring extra batteries, extra calculators. It is your responsibility to bring a workable calculator. • NO cell phone or PDA • Your instructor/TA will not answer any question related to calculators.

  7. Expectations • Use equal signs • Simplify your answers. • Provide units. • Check and Double Check your solutions. • Show the “formula” steps. • For word problems in B.2, show all 5 steps

  8. Steps for Word Problems 1. Draw a diagram 2. Define the variables 3. Write down all the information in terms of the variables defined 4. Set up a relation between the variables 5. Use differentiation to find the related rate. Formally answer the question.

  9. Major Themes:

  10. Slope of the tangent line • Slope of the tangent line at a point on a graph can be approximated by a limiting process. (The same apply to other rate of change problems in physical sciences.)

  11. Tangent Lines y • To define the tangent line at x=1, we pick a point close by. • We can find the secant line of the two points • We can move the point closer and closer to x=1. x 1

  12. Rate of Change y = distance dropped (ft) x = time (s) Find the average speed from x=2 to x=3.

  13. Derivative • Fora function y=f(x), the derivative at x is a function f’ defined by if it exists. (f is differentiable at x f’(x)=The slope of the tangent line at x)

  14. Limit Laws Summary

  15. Simplify

  16. Multiply by conjugate

  17. Differentiation Formulas

  18. Constant Function Rule • If , then • Why?

  19. Constant Multiple Rule If , then where is a constant

  20. Power Rule If , then (n can be any real number)

  21. Sum and Difference Rule • If , then

  22. Product Rule If , then

  23. Quotient Rule If then

  24. Chain Rule

  25. Extended Power Rule

  26. Important Concepts • Left-hand limits and right-hand limits • exists if • f is continuous at a point if • f is differentiable at a point if exists

  27. Important Skills • Evaluate limits by using algebra. • Finding derivatives using limits and formula. • Understand and able to perform implicit differentiation. • Solve word problems.

  28. Remarks • Portion of points are designated for simplifying the answers. • Units are required for some answers.

  29. Remarks • Review quiz solutions.

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