Explanation Given data: y The given limits are: (i) L 1 ( x ) = lim x → ∞ 2 x , (ii) L 2 ( x ) = lim x → ∞ x − 5 , (iii) L 3 ( x ) = lim x → − ∞ e 3 x , (iv) L 4 ( x ) = lim x → 0 1 x 2 , (v) L 5 ( x ) = lim x → 0 + ln x , (vi) L 6 ( x ) = lim x → ∞ ( 1 2 ) x , (vii) L 7 ( x ) = lim x → π 2 tan x , (viii) L 8 ( x ) = lim x → ∞ sin x , (ix) L 9 ( x ) = lim x → ∞ log 1 / 2 x , Methodused: The solution/s of a function are the values of “ x ” for which g ( x ) = 0 , and function g ( x ) does not exist at the point that makes it indefinite. Calculation: The graph of the functions for which the limit is to be calculated in figures here. From the graphs we can observe the limits that are: (i) L 1 ( x ) = lim x → ∞ 2 x = ∞ , does not because as x → ∞ graph becomes parallel to vertical axis. (ii) L 2 ( x ) = lim x → ∞ x − 5 = 0 ,because as x → ∞ the graph becomes along ± x-axis. (iii) L 3 ( x ) = lim x → − ∞ e 3 x = 0 ,because as x → ∞ the graph becomes along -x-axis. (iv) L 4 ( x ) = lim x → 0 1 x 2 , limit does not exist as x → ∞ graph becomes parallel to vertical axis

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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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 3.6, Problem 2TB

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To evaluate: The given limits, using graphs of the functions.

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Chapter 3.6, Problem 1TB

Chapter 3.6, Problem 0C

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3. Differentiate the following functions. Show your work where applicable. a) y = e³x b) f(x)=2 cos(5x) c) y = 1 - 2 d) y = In|secx| e) f(t) = t² e√t f) f(x) = 1+x x sin x 3

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The given limits, using graphs of the functions.

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