Explanation Given information: The expression lim x → 0 + ( 1 + x ) 1 / x x x . Formula used: The limit of quotient of two functions f ( x ) and g ( x ) is the quotient of limit of both the functions. Mathematically, lim x → a f ( x ) g ( x ) = [ lim x → a f ( x ) ] [ lim x → a g ( x ) ] , provided [ lim x → a g ( x ) ] ≠ 0 . Calculation: Consider the expression lim x → 0 + ( 1 + x ) 1 / x x x . Follow the steps mentioned below, to estimate the expression lim x → 0 ( 1 + x ) 1 / x (Exercise 1) Step 1. Press Y = key. Step 2. Enter the expression ( 1 + x ) ^ ( 1 / x ) . Step 3: Press 2 n d key and then WINDOW key. Step 4: With help of arrow key select the option Ask under the Indpnt and press ENTER key. Step 5: Press 2 n d key and then GRAPH key. Step 6: Enter the values of X as 0.1 and press ENTER key. Step 7: Enter the values of X as 0.01 and press ENTER key. Step 8: Enter the values of X as 0.001 and press ENTER key. Step 9: Enter the values of X as 0.0001 and press ENTER key. The output obtained is provided below, Therefore, when x = 0.1 , value of expression is 2.594 , at x = 0.01 , value of expression is 2.705 at x = 0.001 , value of expression is 2.717 and at x = 0.0001 , value of expression is 2.718 . Therefore, the value of the expression, lim x → 0 ( 1 + x ) 1 / x seems to be 2.718 = e . Follow the steps mentioned below, to estimate the expression lim x → 0 + x x . Exercise 4. Step 1. Press Y = key. Step 2. Enter the expression x ^ x . Step 3: Press 2 n d key and then WINDOW key. Step 4: With help of arrow key select the option Ask under the Indpnt and press ENTER key

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists

3rd Edition

ISBN: 9780840064189

Author: Frederick R. Adler

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 2.2, Problem 12E

To determine

To calculate: The value of the expression, limx→0+(1+x)1/xxx with help of Exercise 1 and 4 also describe the construction of the function.

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Chapter 2.2, Problem 11E

Chapter 2.2, Problem 13E

Chapter 2 Solutions

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists

Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E

Ch. 2.1 - Prob. 11E Ch. 2.1 - Prob. 12E Ch. 2.1 - Prob. 13E Ch. 2.1 - Prob. 14E Ch. 2.1 - Prob. 15E Ch. 2.1 - Prob. 16E Ch. 2.1 - Prob. 17E Ch. 2.1 - Prob. 18E Ch. 2.1 - Prob. 19E Ch. 2.1 - Prob. 20E Ch. 2.1 - Prob. 21E Ch. 2.1 - Prob. 22E Ch. 2.1 - Prob. 23E Ch. 2.1 - Prob. 24E Ch. 2.1 - Prob. 25E Ch. 2.1 - Prob. 26E Ch. 2.1 - Prob. 27E Ch. 2.1 - Prob. 28E Ch. 2.1 - Prob. 29E Ch. 2.1 - Prob. 30E Ch. 2.1 - Prob. 31E Ch. 2.1 - Prob. 32E Ch. 2.1 - Prob. 33E Ch. 2.1 - Prob. 34E Ch. 2.1 - Prob. 35E Ch. 2.1 - Prob. 36E Ch. 2.1 - Prob. 37E Ch. 2.1 - Prob. 38E Ch. 2.1 - Prob. 39E Ch. 2.1 - Prob. 40E Ch. 2.1 - Prob. 41E Ch. 2.1 - Prob. 42E Ch. 2.1 - Prob. 43E Ch. 2.1 - Prob. 44E Ch. 2.1 - Prob. 45E Ch. 2.1 - Prob. 46E Ch. 2.2 - Prob. 1E Ch. 2.2 - Prob. 2E Ch. 2.2 - Prob. 3E Ch. 2.2 - Prob. 4E Ch. 2.2 - Prob. 5E Ch. 2.2 - Prob. 6E Ch. 2.2 - Prob. 7E Ch. 2.2 - Prob. 8E Ch. 2.2 - Prob. 9E Ch. 2.2 - Prob. 10E Ch. 2.2 - Prob. 11E Ch. 2.2 - Prob. 12E Ch. 2.2 - Prob. 13E Ch. 2.2 - Prob. 14E Ch. 2.2 - 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The value of the expression, lim x → 0 + ( 1 + x ) 1 / x x x with help of Exercise 1 and 4 also describe the construction of the function.

Solution Summary: The author explains how to calculate the value of the expression, undersetxto amathrmlim(1+x

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To calculate: The value of the expression, limx→0+(1+x)1/xxx with help of Exercise 1 and 4 also describe the construction of the function.

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Chapter 2 Solutions