P09 - possible value depending upon how fast one grows...

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Project 9 MAC 2311 In this project, we will look at a couple of misconceptions about asymptotes and the form “ ∞ - ∞ ”. 1. Some students believe that a graph cannot intersect its horizontal asymp- totes. Consider the following: Write the equation(s) of the horizontal asymptote(s) of the graph of the function f ( x ) = 1 - x 2 x 2 + 2 x . How do you find the points of intersection of the graphs of two equations? Find the point at which f ( x ) intersects its horizontal asymptote(s). Calculate the equation(s) of the horizontal asymptote(s) of the graph of g ( x ) = sin( x ) x using Squeeze Theorem. How many times does the graph of g ( x ) intersect its horizontal asymptote(s)? 1
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2. Some students believe that a if f ( x ) and g ( x ) have limit + as x a , then the limit of f ( x ) - g ( x ) as x a is 0. In actuality, one could have any
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Unformatted text preview: possible value depending upon how fast one grows relative to the other. This is why “ ∞-∞ ” is called an indeterminate form . Consider the following: When x is a very large number, how much difference is there between the numbers x and x 3 ? between √ x and √ x + 1? Justify your conclusion with a few large x values. x x x 3 x √ x √ x + 1 Conclusion: Conclusion: Graph the functions on the axes as indicated below: y = x and y = x 3 y = √ x and y = √ x + 1 Calculate the limits using the methods outlined in class. lim x →∞ x 3-x lim x →∞ √ x + 1-√ x Do these two limits agree with your conclusions above? Now evaluate the “ ∞ - ∞ ” form: lim x →∞ p x 2 + 4 x-x 2...
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This note was uploaded on 01/13/2010 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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P09 - possible value depending upon how fast one grows...

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