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Math 2413 Calculus I David Dippel 2.1 and 2.2

Math 2413 Calculus I David Dippel 2.1 and 2.2. What is Calculus?. The Mathematics of change. Without Calculus With Calculus. Length of a curve. Length of a segment. Area under a curve. Geometric area. Slope of a curve. Slope of a line. Instantaneous velocity.

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Math 2413 Calculus I David Dippel 2.1 and 2.2

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  1. Math 2413Calculus IDavid Dippel2.1 and 2.2

  2. What is Calculus? The Mathematics of change Without Calculus With Calculus Length of a curve Length of a segment Area under a curve Geometric area Slope of a curve Slope of a line Instantaneous velocity Average velocity

  3. Average Velocity A ball is thrown upward with a velocity of 90 ft/sec. Find the formula for the position of the rock and the average velocity bewteen t = 1 and t = 2 seconds.

  4. Average Velocity If the position function for an object in motion is: s(t) = -16t2 + 55t, find the average velocity for each interval:

  5. Fill in the table to find the Instantaneous Velocity 1 1.5 1.9 1.99 1.99 2

  6. Section 2.2Finding Limits Graphicallyand Numerically

  7. Limits Graphically Means as x approaches the constant c from the right, f(x) approaches L. Means as x approaches the constant c from the left, f(x) aproaches L. Means the right and left sides are the same.

  8. Examples: 4 2 2 No Limit -3 2 2 No Limit No Limit

  9. Draw a graph that has the following limits and values

  10. Fill in the table to find the limit -3 -3.19 -3.02 -3.002 -2.998 -2.98 -2.79

  11. Review of Limit Notation X 4 is what the _______ value approaches 5 is the ________ value approaches + tells that you come from the _______ Y Right

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