Example 3: The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s (t) = 2 sin at + 3 cos at , where t is measured in seconds. (a) Find the average velocity during each time period to four decimal places: (i) [1,2]: Done in class. We got 6 cm/sec. (ii) [1, 1.1] (iii) [1, 1.01] (iv) [1,1.001] (b) Estimate the instantaneous velocity of the particle when t=1 to four decima places.

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A: Find the equation of the line that is tangent to y = ln x at x = 1.

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.