MATH 1010U Lecture Notes - Lecture 6: Riemann Sum, Prentice Hall, Antiderivative
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Sometimes, it is difficult or impossible to find the antiderivative of a function, but we can still gather info about it graphically. A direction field, which shows the slope at given points, can be used to sketch a graph of the antiderivative of a function. Example: if the direction field corresponding to to is given below, sketch subject xf. Example: in each of the graphs below, determine which curve is is (the antiderivative of. Exercise (application): suppose the rate of change of concentration of a vitamin in the bloodstream at time t is given by dc dt. [source: modified from calculus for biology and medicine by claudia neuhauser, 2nd ed. , prentice hall, 2004] Application: a ball is thrown upward with a speed of 10 m/s from a building that is 30m tall. Find a formula describing the height of the ball above the ground t seconds later.
