Homework Help is Here – Start Your Trial Now!
Math
Calculus
Assume that I and M are real numbers such that lim_f(x) = L and lim_g(x) = M. Let c be x→a x→a a constant. Then, each of the following statements holds Which of the following limit law statements is incorrect? ƒ(x))” ○ lim (f(x))" x→a lim ○ lim (f(x) + g(x)) x→a x→a = lim f(x) g(x) x→a = ○ lim (f(x) · g(x)) x→a lim f(x) x → a lim g(x) x→a = lim f(x) + lim_g(x) = L + M x→a x → a = L. M L" for every positive integer n lim f(x) lim_ g(x) = L · M x→a x→a .

Assume that I and M are real numbers such that lim_f(x) = L and lim_g(x) = M. Let c be x→a x→a a constant. Then, each of the following statements holds Which of the following limit law statements is incorrect? ƒ(x))” ○ lim (f(x))" x→a lim ○ lim (f(x) + g(x)) x→a x→a = lim f(x) g(x) x→a = ○ lim (f(x) · g(x)) x→a lim f(x) x → a lim g(x) x→a = lim f(x) + lim_g(x) = L + M x→a x → a = L. M L" for every positive integer n lim f(x) lim_ g(x) = L · M x→a x→a .

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...
See similar textbooks
Question
Assume that \( L \) and \( M \) are real numbers such that \[ \lim_{x \to a} f(x) = L \quad \text{and} \quad \lim_{x \to a} g(x) = M. \] Let \( c \) be a constant. Then, each of the following statements holds: **Which of the following limit law statements is incorrect?** 1. \(\circ\) \(\lim_{x \to a} \left( f(x) \right)^n = \left( \lim_{x \to a} f(x) \right)^n = L^n\) for every positive integer \( n \). 2. \(\circ\) \(\lim_{x \to a} \left( f(x) + g(x) \right) = \lim_{x \to a} f(x) + \lim_{x \to a} g(x) = L + M\). 3. \(\circ\) \(\lim_{x \to a} \left( \frac{f(x)}{g(x)} \right) = \frac{\lim_{x \to a} f(x)}{\lim_{x \to a} g(x)} = L \cdot M\). 4. \(\circ\) \(\lim_{x \to a} \left( f(x) \cdot g(x) \right) = \lim_{x \to a} f(x) \cdot \lim_{x \to a} g(x) = L \cdot M\).
Transcribed Image Text:Assume that \( L \) and \( M \) are real numbers such that \[ \lim_{x \to a} f(x) = L \quad \text{and} \quad \lim_{x \to a} g(x) = M. \] Let \( c \) be a constant. Then, each of the following statements holds: **Which of the following limit law statements is incorrect?** 1. \(\circ\) \(\lim_{x \to a} \left( f(x) \right)^n = \left( \lim_{x \to a} f(x) \right)^n = L^n\) for every positive integer \( n \). 2. \(\circ\) \(\lim_{x \to a} \left( f(x) + g(x) \right) = \lim_{x \to a} f(x) + \lim_{x \to a} g(x) = L + M\). 3. \(\circ\) \(\lim_{x \to a} \left( \frac{f(x)}{g(x)} \right) = \frac{\lim_{x \to a} f(x)}{\lim_{x \to a} g(x)} = L \cdot M\). 4. \(\circ\) \(\lim_{x \to a} \left( f(x) \cdot g(x) \right) = \lim_{x \to a} f(x) \cdot \lim_{x \to a} g(x) = L \cdot M\).
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS