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

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Expectations

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

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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

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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.

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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.

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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

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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.

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Major Themes:

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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.)

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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

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

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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)

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Limit Laws Summary

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Simplify

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Multiply by conjugate

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Differentiation Formulas

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Constant Function Rule If, then Why?

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Constant Multiple Rule If, then where is a constant

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

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Sum and Difference Rule If, then

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Product Rule If, then

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Quotient Rule If then

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Chain Rule

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Extended Power Rule

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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

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

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

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Remarks Review quiz solutions.

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MAT 1221 Survey of Calculus Section 2.3 Rates of Change

MAT 1221 Survey of Calculus Section 2.3 Rates of Change

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