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Find each of the following limits. sin x + tan x 1. lim 1- cos?x 2. lim x2 e2x + x ex +1 3. lim X00

Find each of the following limits. sin x + tan x 1. lim 1- cos?x 2. lim x2 e2x + x ex +1 3. lim X00

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
**Transcription for Educational Website** Title: Calculating Limits Instructions: Find each of the following limits. 1. \( \lim_{x \to 0} \frac{\sin x + \tan x}{x} \) 2. \( \lim_{x \to 0} \frac{1 - \cos 2x}{x^2} \) 3. \( \lim_{x \to \infty} \frac{e^{2x} + x}{e^x + 1} \) 4. \( \lim_{x \to \infty} \frac{x + \ln (4x)}{x^2} \) 5. \( \lim_{x \to \infty} \frac{\sqrt{x + 1}}{1 + \ln (2x)} \) These exercises involve evaluating limits, which are fundamental concepts in calculus, especially as they relate to analyzing the behavior of functions as they approach certain points or infinity.
Transcribed Image Text:**Transcription for Educational Website** Title: Calculating Limits Instructions: Find each of the following limits. 1. \( \lim_{x \to 0} \frac{\sin x + \tan x}{x} \) 2. \( \lim_{x \to 0} \frac{1 - \cos 2x}{x^2} \) 3. \( \lim_{x \to \infty} \frac{e^{2x} + x}{e^x + 1} \) 4. \( \lim_{x \to \infty} \frac{x + \ln (4x)}{x^2} \) 5. \( \lim_{x \to \infty} \frac{\sqrt{x + 1}}{1 + \ln (2x)} \) These exercises involve evaluating limits, which are fundamental concepts in calculus, especially as they relate to analyzing the behavior of functions as they approach certain points or infinity.
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