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lim x→0 6e4a-2e3a-4 sin (2x) (A) B C D 2 4 9 18

lim x→0 6e4a-2e3a-4 sin (2x) (A) B C D 2 4 9 18

Calculus: Early Transcendentals
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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Question
The image presents a calculus problem involving limits: \[ \lim_{{x \to 0}} \frac{{6e^{4x} - 2e^{3x} - 4}}{{\sin(2x)}} = \] Options are provided for the solution: - Option A: 2 - Option B: 4 - Option C: 9 - Option D: 18 No graphs or diagrams are included, only the mathematical expression and multiple-choice options.
Transcribed Image Text:The image presents a calculus problem involving limits: \[ \lim_{{x \to 0}} \frac{{6e^{4x} - 2e^{3x} - 4}}{{\sin(2x)}} = \] Options are provided for the solution: - Option A: 2 - Option B: 4 - Option C: 9 - Option D: 18 No graphs or diagrams are included, only the mathematical expression and multiple-choice options.
Let \( f \) be the function defined by \( f(x) = 2x + 3e^{-5x^2} \), and let \( g \) be a differentiable function with derivative given by \( g'(x) = \frac{1}{x} + 4 \cos \left( \frac{5}{x} \right) \). It is known that \( \lim_{x \to \infty} g(x) = \infty \). The value of \( \lim_{x \to \infty} \frac{f(x)}{g(x)} \) is A. 0 B. \( \frac{1}{2} \) C. 1 D. nonexistent
Transcribed Image Text:Let \( f \) be the function defined by \( f(x) = 2x + 3e^{-5x^2} \), and let \( g \) be a differentiable function with derivative given by \( g'(x) = \frac{1}{x} + 4 \cos \left( \frac{5}{x} \right) \). It is known that \( \lim_{x \to \infty} g(x) = \infty \). The value of \( \lim_{x \to \infty} \frac{f(x)}{g(x)} \) is A. 0 B. \( \frac{1}{2} \) C. 1 D. nonexistent
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