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MAT 1221 Survey of Calculus Exam 1 Info

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1 MAT 1221 Survey of Calculus Exam 1 Info

2 Expectations

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, , 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 x Tangent Lines 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. y 1

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

13 Derivative For a 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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