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MATH 1115

by: Mrs. Kara Jacobs
Mrs. Kara Jacobs
GPA 3.59

Laurie Edler

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Laurie Edler
Class Notes
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This 6 page Class Notes was uploaded by Mrs. Kara Jacobs on Monday October 12, 2015. The Class Notes belongs to MATH 1115 at Georgia College & State University taught by Laurie Edler in Fall. Since its upload, it has received 56 views. For similar materials see /class/221928/math-1115-georgia-college-state-university in Mathematics (M) at Georgia College & State University.

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Date Created: 10/12/15
Math 1115 1 Dr Huffman 2728 Tangents Velocities Other Rates of Change and Derivatives Let x1fx1xzfx2 be two points on the graph of a function The slope of the secant f2 7 line between these two points is given by msec m2 7 m1 Example 1 Let 2 Find the slope of the secant line between the points 17 and 27112 Example 2 Find the slope of the tangent line to the graph of 2 at m 1 Example 3 Suppose a particle is moving along a straight line and its directed distance measured in meters at time t is given by 805 t2 a How far has the object traveled after 1 second b How far has the object traveled after 2 seconds C Is the object s speed constant d What is the difference between the objects speed and the object s velocity Math 1115 2 Dr Huffman e What is the average velocity of the particle from t l to t 2seconds In general7 the average velocity over the interval from t1 to 752 is given by Chan e in osition average veloezty A change in time t 7 75 average velocity w 752 7 751 f Describe the trend of the average velocities calculated in the table below Express this trend using a one sided limit Time Interval Average Velocity t1tot2 52 51 2 l t1tot15 5 51 l t1tot11 5 51 t1tot101 5 51 Math 1115 3 Dr Huffman g What is the average velocity of the particle from t 0 to t 1seconds h Describe the trend of the average velocities calculated in the table below Express this trend using a one sided limit Time Interval Average Velocity t0tot1 SUD 51 0 1 t05tot1 5 51 1 t09tot1 5 51 1 t099tot1 5 51 1 How can we describe the behavior of the average velocity of the particle as t approaches 1 using a general limit Math 1115 4 Dr Huffman For any value of t we have that 875 i 51 avera e velocit g y t i 1 Math 1115 5 Dr Huffman Let 8t describe the position of a particle moving in a straight line Then the instantaneous velocity of the particle at time t a is given by if this limit exists Let us now explore the concept of tangent line to the graph of any function Math 1115 Dr Huffman What is the relationship between the slope of the tangent line to the graph at t a and the instantaneous velocity of the particle at t a 7 What is the relationship between the slope of the tangent line to the graph at t a and the rate of change of the position function at t a 7 These concepts can be generalized to any function The derivative of a function f at a number a denoted by f39a is we as 7 a if this limit exits Calculate f39l for the function 2


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