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Find the following limits. Justify any use of L'Hopital's rule. Show all work toward your answer. ex x48x² a. lim b. lim xả5x-50 x-10 x-10

Find the following limits. Justify any use of L'Hopital's rule. Show all work toward your answer. ex x48x² a. lim b. lim xả5x-50 x-10 x-10

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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## Problem 7: Calculating Limits Find the following limits. Justify any use of L'Hopital's rule. Show all work toward your answer. ### a. \(\lim_{x \to \infty} \frac{e^x}{x^2}\) ### b. \(\lim_{x \to 10} \frac{x^2 - 5x - 50}{x - 10}\) #### Explanation: - **L'Hopital's Rule**: Apply this rule when evaluating limits that result in indeterminate forms such as \(\frac{0}{0}\) or \(\frac{\infty}{\infty}\). - Each limit should be calculated step-by-step, clearly showing differentiation if L'Hopital's Rule is used, and simplifying when possible. ### Graph Details The image contains a graph above the text, though it is not directly related to the specific problem prompts given in the transcription. It features a grid with vertical measurements marked from -10 to 8. However, specific curves or data points are not detailed or described.
Transcribed Image Text:## Problem 7: Calculating Limits Find the following limits. Justify any use of L'Hopital's rule. Show all work toward your answer. ### a. \(\lim_{x \to \infty} \frac{e^x}{x^2}\) ### b. \(\lim_{x \to 10} \frac{x^2 - 5x - 50}{x - 10}\) #### Explanation: - **L'Hopital's Rule**: Apply this rule when evaluating limits that result in indeterminate forms such as \(\frac{0}{0}\) or \(\frac{\infty}{\infty}\). - Each limit should be calculated step-by-step, clearly showing differentiation if L'Hopital's Rule is used, and simplifying when possible. ### Graph Details The image contains a graph above the text, though it is not directly related to the specific problem prompts given in the transcription. It features a grid with vertical measurements marked from -10 to 8. However, specific curves or data points are not detailed or described.
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