a. Explanation Given: It is given in the question that function of f(x) is f ( x ) = e x Concept Used: In this we must use the concept of derivatives. Wemust use the formula of lim x → 0 e x − 1 x = 1 . Calculation: The graph of the function f ( x ) = e x is shown in the figure. Notice that the graph crosses the y − axis with a slope of 1 b. To determine Find which type of function is f ( x ) = e x and g ( x ) = x e .Compare the differentiation . c. To determine Find whether the two function in part (b) grows more rapidly when x is large.

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Chapter 3, Problem 2E

To determine

Draw the graph of the function f(x)=ex .Show the facts.

To determine

Find which type of function is f(x)=ex and g(x)=xe .Compare the differentiation.

To determine

Find whether the two function in part (b) grows more rapidly when x is large.

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Chapter 3, Problem 1E

Chapter 3, Problem 3E

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5:38 Video Message instructor Submit Question ||| D

8:38 *** TEMU TEMU -3 -2 7 B 2 1 & 5G. 61% 1 2 -1 Based on the graph above, determine the amplitude, period, midline, and equation of the function. Use f(x) as the output. Amplitude: 2 Period: 2 Midline: 2 ☑ syntax error: this is not an equation. Function: f(x) = −2 cos(πx + 2.5π) +2× Question Help: Worked Example 1 ☑ Message instructor Submit Question ||| <

8:39 *** TEMU 5G 60% A ferris wheel is 28 meters in diameter and boarded from a platform that is 2 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 4 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. What is the amplitude? 14 meters What is the equation of the Midline? y = 16 What is the period? 4 meters minutes The equation that models the height of the ferris wheel after t minutes is: f(t): = ƒ (3) = ·−14(0) + 16 syntax error: you gave an equation, not an expression. syntax error. Check your variables - you might be using an incorrect one. How high are you off of the ground after 3 minutes? Round your answe the nearest meter. ||| <

Chapter 3 Solutions

Biocalculus

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Draw the graph of the function f ( x ) = e x .Show the facts.

Solution Summary: The author illustrates how the graph of the function f(x)=ex crosses the y axis with a slope of 1.

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Draw the graph of the function f(x)=ex .Show the facts.

Find which type of function is f(x)=ex and g(x)=xe .Compare the differentiation.

Find whether the two function in part (b) grows more rapidly when x is large.

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Chapter 3 Solutions