Explanation l’Hôpital’s Rule: Suppose f and g are differentiable on an open interval I that contains a , with possible exception of a itself and g ′ ( x ) ≠ 0 for all x in I , with possible exception of a . if lim x → a f ( x ) g ( x ) has an indeterminate form of the type 0 0 or ∞ ∞ , then lim x → a f ( x ) g ( x ) = lim x → a f ′ ( x ) g ′ ( x ) provided that the limit on the right or is infinite. Calculation: Obtain the value of limit lim m → ∞ P ( 1 + r m ) m t , Let y = lim m → ∞ P ( 1 + r m ) m t , Divide by r on both the numerator and denominator, y = lim m → ∞ P ( 1 + 1 m r ) m t y = lim m → ∞ P ( 1 + 1 m r

The limit using l’Hôpital’s Rule.

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage Learning

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…

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Chapter B, Problem 30E

To determine

To evaluate: The limit using l’Hôpital’s Rule.

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Use a graphing calculator to answer the following questions. a. From a graph of y=xex, what do you think is the value of limxxex?Support this by evaluating the function for several large values of x. b. Repeat part a, this time using the graph of y=x2ex. c. Based on your results from parts a and b, what do you think is the value of limxxnex, where n is a positive integer?Support this by experimenting with other positive integer n.

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