**Transcription for Educational Website:****a. For what values of $ b > 0 $ does $ b^x $ grow faster than $ e^x $ as $ x \to \infty $? b. Compare the growth rates of $ e^x $ and $ e^{ax} $ as $ x \to \infty $ for $ a > 0 $.**---**a. Choose the correct answer below.**- **A.** When $ b < 1 $, $ b^x $ grows faster than $ e^x $ as $ x \to \infty $.- **B.** When $ b < e $, $ b^x $ grows faster than $ e^x $ as $ x \to \infty $.- **C.** When $ b > 1 $, $ b^x $ grows faster than $ e^x $ as $ x \to \infty $.- **D.** When $ b > e $, $ b^x $ grows faster than $ e^x $ as $ x \to \infty $.---**b. Choose the correct answer below.**- **A.** The expression $ e^x $ grows faster than $ e^{ax} $ as $ x \to \infty $ for $ a > 0 $, where $ a \neq 1 $.- **B.** The expression $ e^{ax} $ grows slower than $ e^x $ as $ x \to \infty $ for $ a > 0 $, where $ a \neq 1 $.- **C.** The expression $ e^x $ grows faster than $ e^{ax} $ as $ x \to \infty $ for $ a > 1 $; $ e^{ax} $ grows slower than $ e^x $ as $ x \to \infty $ for $ 0 < a < 1 $.- **D.** The expression $ e^{ax} $ grows slower than $ e^x $ as $ x \to \infty $ for $ a > 1 $; $ e^{ax} $ grows faster than $ e^x $ as \( x \

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a. For what values of b>0 does b* grow faster than e* as x→00? ах b. Compare the growth rates of ex and e as x0o for a>0. a. Choose the correct answer below. O A. When b<1, b* grows faster than e* as x0o. O B. When b1, b* grows faster than e* as x0o. O D. When b>e, b* grows faster than e* as x→0o. b. Choose the correct answer below. O A. The expression e ax grows faster than e* as x→0o for a > 0, where a+ 1. O B. The expression e ax grows slower than e as x0o for a > 0, where a+ 1. O C. The expression e ax grows faster than e* as x-00 for a> 1; e ax grows slower than e* as x→0o for 0 1; e ax grows faster than e* as x→0o for 0

a. For what values of b>0 does b* grow faster than e* as x→00? ах b. Compare the growth rates of ex and e as x0o for a>0. a. Choose the correct answer below. O A. When b<1, b* grows faster than e* as x0o. O B. When b1, b* grows faster than e* as x0o. O D. When b>e, b* grows faster than e* as x→0o. b. Choose the correct answer below. O A. The expression e ax grows faster than e* as x→0o for a > 0, where a+ 1. O B. The expression e ax grows slower than e as x0o for a > 0, where a+ 1. O C. The expression e ax grows faster than e* as x-00 for a> 1; e ax grows slower than e* as x→0o for 0 1; e ax grows faster than e* as x→0o for 0

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

**Transcription for Educational Website:**

**a. For what values of $ b > 0 $ does $ b^x $ grow faster than $ e^x $ as $ x \to \infty $?
b. Compare the growth rates of $ e^x $ and $ e^{ax} $ as $ x \to \infty $ for $ a > 0 $.**

---

**a. Choose the correct answer below.**

- **A.** When $ b < 1 $, $ b^x $ grows faster than $ e^x $ as $ x \to \infty $.

- **B.** When $ b < e $, $ b^x $ grows faster than $ e^x $ as $ x \to \infty $.

- **C.** When $ b > 1 $, $ b^x $ grows faster than $ e^x $ as $ x \to \infty $.

- **D.** When $ b > e $, $ b^x $ grows faster than $ e^x $ as $ x \to \infty $.

---

**b. Choose the correct answer below.**

- **A.** The expression $ e^x $ grows faster than $ e^{ax} $ as $ x \to \infty $ for $ a > 0 $, where $ a \neq 1 $.

- **B.** The expression $ e^{ax} $ grows slower than $ e^x $ as $ x \to \infty $ for $ a > 0 $, where $ a \neq 1 $.

- **C.** The expression $ e^x $ grows faster than $ e^{ax} $ as $ x \to \infty $ for $ a > 1 $; $ e^{ax} $ grows slower than $ e^x $ as $ x \to \infty $ for $ 0 < a < 1 $.

- **D.** The expression $ e^{ax} $ grows slower than $ e^x $ as $ x \to \infty $ for $ a > 1 $; $ e^{ax} $ grows faster than $ e^x $ as \( x \

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