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x = 2. (a) lim Below is the graphs of f(x) and g(x), and their tangent lines at YA y = 1.8(x-2) 0 x + 2 sin x 1-0 3 tan x- x2 (c) lim Use L'Hospital rule to evaluate each limit. 5r2+6 100 3e + 11 2 f X 4 y=(x-2) (b) lim g(x) f(x) (d) lim (1+x)= I-0+

x = 2. (a) lim Below is the graphs of f(x) and g(x), and their tangent lines at YA y = 1.8(x-2) 0 x + 2 sin x 1-0 3 tan x- x2 (c) lim Use L'Hospital rule to evaluate each limit. 5r2+6 100 3e + 11 2 f X 4 y=(x-2) (b) lim g(x) f(x) (d) lim (1+x)= I-0+

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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Below are the graphs of \( f(x) \) and \( g(x) \), and their tangent lines at \( x = 2 \). **Graph Description:** - The graph includes two functions, \( f(x) \) and \( g(x) \). - The tangent line to \( f(x) \) at \( x = 2 \) is represented by the equation \( y = 1.8(x - 2) \). - The tangent line to \( g(x) \) at \( x = 2 \) is represented by the equation \( y = \frac{4}{5}(x - 2) \). **Axes:** - The horizontal axis is labeled \( x \). - The vertical axis is labeled \( y \). - The point of tangency on both graphs occurs at \( x = 2 \). **Function Behavior:** - \( f(x) \) is depicted as a magenta curve with its tangent line being more steep. - \( g(x) \) is depicted as a cyan curve with its tangent line being less steep compared to \( f(x) \). **Instructions:** Use L'Hospital's rule to evaluate each limit. **Limit Problems:** (a) \(\lim_{x \to 0} \frac{x + 2 \sin x}{3 \tan x - x^2}\) (b) \(\lim_{x \to 2} \frac{g(x)}{f(x)}\) (c) \(\lim_{x \to \infty} \frac{5x^2 + 6}{3e^x + 11}\) (d) \(\lim_{x \to 0^+} \left(1 + x\right)^{\frac{3}{x}}\)
Transcribed Image Text:Below are the graphs of \( f(x) \) and \( g(x) \), and their tangent lines at \( x = 2 \). **Graph Description:** - The graph includes two functions, \( f(x) \) and \( g(x) \). - The tangent line to \( f(x) \) at \( x = 2 \) is represented by the equation \( y = 1.8(x - 2) \). - The tangent line to \( g(x) \) at \( x = 2 \) is represented by the equation \( y = \frac{4}{5}(x - 2) \). **Axes:** - The horizontal axis is labeled \( x \). - The vertical axis is labeled \( y \). - The point of tangency on both graphs occurs at \( x = 2 \). **Function Behavior:** - \( f(x) \) is depicted as a magenta curve with its tangent line being more steep. - \( g(x) \) is depicted as a cyan curve with its tangent line being less steep compared to \( f(x) \). **Instructions:** Use L'Hospital's rule to evaluate each limit. **Limit Problems:** (a) \(\lim_{x \to 0} \frac{x + 2 \sin x}{3 \tan x - x^2}\) (b) \(\lim_{x \to 2} \frac{g(x)}{f(x)}\) (c) \(\lim_{x \to \infty} \frac{5x^2 + 6}{3e^x + 11}\) (d) \(\lim_{x \to 0^+} \left(1 + x\right)^{\frac{3}{x}}\)
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