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Find the limits. Show your steps. x²-9 x 3 x²7x+12 (a) lim (b) lim x 3 x 3 (c) lim h-0 √1+h-1 h

Find the limits. Show your steps. x²-9 x 3 x²7x+12 (a) lim (b) lim x 3 x 3 (c) lim h-0 √1+h-1 h

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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### Limit Problems In this section, we will find the limits of given functions. Follow the steps to solve each problem. #### 1. Find the limits. Show your steps. **(a)** \(\lim_{{x \to 3}} \frac{{x^2 - 9}}{{x^2 - 7x + 12}}\) **(b)** \(\lim_{{x \to 3}} \frac{{\frac{1}{x} - \frac{1}{3}}}{{x - 3}}\) **(c)** \(\lim_{{h \to 0}} \frac{{\sqrt{1 + h} - 1}}{{h}}\) ### Explanation of Graphs or Diagrams In this question, there are three mathematical limit problems to solve, each presented in equation form. There are no graphs or diagrams associated with these problems. Each part presents a different scenario involving limits, including polynomial fractions, rational expressions with variables in the numerator and denominator, and expressions involving square roots. Each one requires a step-by-step approach to find the limit as the variable approaches a specific value.
Transcribed Image Text:### Limit Problems In this section, we will find the limits of given functions. Follow the steps to solve each problem. #### 1. Find the limits. Show your steps. **(a)** \(\lim_{{x \to 3}} \frac{{x^2 - 9}}{{x^2 - 7x + 12}}\) **(b)** \(\lim_{{x \to 3}} \frac{{\frac{1}{x} - \frac{1}{3}}}{{x - 3}}\) **(c)** \(\lim_{{h \to 0}} \frac{{\sqrt{1 + h} - 1}}{{h}}\) ### Explanation of Graphs or Diagrams In this question, there are three mathematical limit problems to solve, each presented in equation form. There are no graphs or diagrams associated with these problems. Each part presents a different scenario involving limits, including polynomial fractions, rational expressions with variables in the numerator and denominator, and expressions involving square roots. Each one requires a step-by-step approach to find the limit as the variable approaches a specific value.
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