My question is , why does this equal 0? I thought the limit was infinity here. ? Because (e^1/10/2)^n I thought was infinity? **Section 10.2: Limits and Exponentials****Problem 10.2.35:**Find the limit:\[\lim_{{n \to \infty}} \tan^{-1} n = \frac{\pi}{2}\]**Problem 10.2.36:**Consider the expression:\[ e^{1/10} = \sqrt[10]{e} \approx 1.1. \]Let \( r = \frac{e^{1/10}}{2} \) and note that \( 0 < r < 1 \).Therefore, \[\lim_{{n \to \infty}} \frac{e^{n/10}}{2^n} = \lim_{{n \to \infty}} r^n = 0.\] This demonstrates how exponential limits can converge to zero when the base of the exponential is less than 1. Certainly! Here is the transcription and explanation suitable for an educational website:---**Question 36:**Evaluate the expression:\[\left\{ \frac{e^{n/10}}{2^n} \right\}\]**Explanation:**This problem involves an exponential function where \( e^{n/10} \) is divided by \( 2^n \). The curly braces suggest that you may need to find the fractional part of the expression for different values of \( n \).**Steps to Consider:**1. **Understand the Function:** - **Numerator:** \( e^{n/10} \) – An exponential function where \( n \) is divided by 10. - **Denominator:** \( 2^n \) – An exponential function with base 2 raised to the power \( n \).2. **Evaluate for sample values of \( n \):** - Substitute specific values for \( n \) to determine the behavior of the function. - Calculate the result and extract the fractional part.3. **Graphical Representation (if required):** - A graph of \( \frac{e^{n/10}}{2^n} \) versus \( n \) may illustrate the convergence behavior or how the fractional part changes.Use this as a guideline to explore the function further and recognize patterns that emerge with different \( n \) values.---

The given data is: e110=e10=1.1 r=e1102, 0<r<1 To find the value of limn→∞en102n

Answered: L0.2.35 lim tan- 7n = 10.2.36 Note that…

L0.2.35 lim tan- 7n = 10.2.36 Note that el/10 = 19e 1.1. Let r = el/10 en/10 and note that 0

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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