Limit Laws If L, M, c, and k are real numbers and limƒ(x)=L and limg(x)= M, then 1. Sum Rule 2. Difference Rule 3. Constant Multiple Rule lim(k-f(x)) =. 4. Product Rule lim(f(x) g(x)) = 5. Quotient Rule 6. Power Rule lim(ƒ(x)+g(x))=. lim(f(x)-g(x)) =. X-C X-C X-C X-C lim X-C X-C X-C f(x) g(x) = lim[ƒ(x)]" = = , M = 0 I n a positive integer 7. Root Rule lim: f(x) = X-C (If n is even, we assume that f(x) ≥ 0 for x in an interval containing c.) Note: If L or M are not finite, then these rules do not apply! n a positive integer I
Limit Laws If L, M, c, and k are real numbers and limƒ(x)=L and limg(x)= M, then 1. Sum Rule 2. Difference Rule 3. Constant Multiple Rule lim(k-f(x)) =. 4. Product Rule lim(f(x) g(x)) = 5. Quotient Rule 6. Power Rule lim(ƒ(x)+g(x))=. lim(f(x)-g(x)) =. X-C X-C X-C X-C lim X-C X-C X-C f(x) g(x) = lim[ƒ(x)]" = = , M = 0 I n a positive integer 7. Root Rule lim: f(x) = X-C (If n is even, we assume that f(x) ≥ 0 for x in an interval containing c.) Note: If L or M are not finite, then these rules do not apply! n a positive integer I
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
![**Limit Laws**
If \( L, M, C, \) and \( k \) are real numbers and \(\lim_{x \to c} f(x) = L\) and \(\lim_{x \to c} g(x) = M\), then:
1. **Sum Rule**
\(\lim_{x \to c} (f(x) + g(x)) = L + M\)
2. **Difference Rule**
\(\lim_{x \to c} (f(x) - g(x)) = L - M\)
3. **Constant Multiple Rule**
\(\lim_{x \to c} (k \cdot f(x)) = kL\)
4. **Product Rule**
\(\lim_{x \to c} (f(x) \cdot g(x)) = L \cdot M\)
5. **Quotient Rule**
\(\lim_{x \to c} \left(\frac{f(x)}{g(x)}\right) = \frac{L}{M}\), \(M \neq 0\)
6. **Power Rule**
\(\lim_{x \to c} (f(x))^n = L^n\), \(n\) a positive integer
7. **Root Rule**
\(\lim_{x \to c} \sqrt[n]{f(x)} = \sqrt[n]{L}\), \(n\) a positive integer
(Note: If \( n \) is even, we assume that \( f(x) \geq 0 \) for \( x \) in an interval containing \( c \).)
**Note:** If \( L \) or \( M \) are not finite, then these rules do not apply.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F739452bb-bec9-43d8-9372-35dc57efa9d5%2Ffb77b19a-afc8-464d-8fbc-78a07651860a%2Fzzwfldn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Limit Laws**
If \( L, M, C, \) and \( k \) are real numbers and \(\lim_{x \to c} f(x) = L\) and \(\lim_{x \to c} g(x) = M\), then:
1. **Sum Rule**
\(\lim_{x \to c} (f(x) + g(x)) = L + M\)
2. **Difference Rule**
\(\lim_{x \to c} (f(x) - g(x)) = L - M\)
3. **Constant Multiple Rule**
\(\lim_{x \to c} (k \cdot f(x)) = kL\)
4. **Product Rule**
\(\lim_{x \to c} (f(x) \cdot g(x)) = L \cdot M\)
5. **Quotient Rule**
\(\lim_{x \to c} \left(\frac{f(x)}{g(x)}\right) = \frac{L}{M}\), \(M \neq 0\)
6. **Power Rule**
\(\lim_{x \to c} (f(x))^n = L^n\), \(n\) a positive integer
7. **Root Rule**
\(\lim_{x \to c} \sqrt[n]{f(x)} = \sqrt[n]{L}\), \(n\) a positive integer
(Note: If \( n \) is even, we assume that \( f(x) \geq 0 \) for \( x \) in an interval containing \( c \).)
**Note:** If \( L \) or \( M \) are not finite, then these rules do not apply.
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