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or the function, evaluate the following. (If an answer does not exist, enter DNE.) д(x, у, 2) In(x + y + z) a) g(0, 0, 0) b) g(1, 0, 0) с) g(0, 1, 0) Ed) g(z, х, у) e) д(x + h, у + k, z + )

or the function, evaluate the following. (If an answer does not exist, enter DNE.) д(x, у, 2) In(x + y + z) a) g(0, 0, 0) b) g(1, 0, 0) с) g(0, 1, 0) Ed) g(z, х, у) e) д(x + h, у + k, z + )

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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### Evaluation of the Function \( g(x, y, z) = \ln(x + y + z) \) Below are the given functions to evaluate. If an answer does not exist, enter DNE (Does Not Exist). #### (a) \( g(0, 0, 0) \) \[ g(0, 0, 0) = \ln(0 + 0 + 0) = \ln(0) \] Since the natural logarithm of zero is undefined, the answer is: DNE. #### (b) \( g(1, 0, 0) \) \[ g(1, 0, 0) = \ln(1 + 0 + 0) = \ln(1) \] Since the natural logarithm of one is zero, the answer is: \[ 0 \] #### (c) \( g(0, 1, 0) \) \[ g(0, 1, 0) = \ln(0 + 1 + 0) = \ln(1) \] Since the natural logarithm of one is zero, the answer is: \[ 0 \] #### (d) \( g(z, x, y) \) \[ g(z, x, y) = \ln(z + x + y) \] Here, the function's form doesn't change; it is simply restructured. #### (e) \( g(x + h, y + k, z + l) \) \[ g(x + h, y + k, z + l) = \ln((x + h) + (y + k) + (z + l)) \] This simplifies to: \[ g(x + h, y + k, z + l) = \ln(x + y + z + h + k + l) \] Here, the inputs are expressed as summing each variable \(x, y, z\) with additional parameters \(h, k, l\). ### Notes - The natural logarithm function \(\ln\) is defined only for positive arguments. When evaluating these functions, ensure the sum \(x + y + z\) is positive; otherwise, the function does not exist (DNE). - Be mindful of the domain restrictions for the logarithmic function when calculating \( g(x, y, z) \). The function \( \ln(x + y + z
Transcribed Image Text:### Evaluation of the Function \( g(x, y, z) = \ln(x + y + z) \) Below are the given functions to evaluate. If an answer does not exist, enter DNE (Does Not Exist). #### (a) \( g(0, 0, 0) \) \[ g(0, 0, 0) = \ln(0 + 0 + 0) = \ln(0) \] Since the natural logarithm of zero is undefined, the answer is: DNE. #### (b) \( g(1, 0, 0) \) \[ g(1, 0, 0) = \ln(1 + 0 + 0) = \ln(1) \] Since the natural logarithm of one is zero, the answer is: \[ 0 \] #### (c) \( g(0, 1, 0) \) \[ g(0, 1, 0) = \ln(0 + 1 + 0) = \ln(1) \] Since the natural logarithm of one is zero, the answer is: \[ 0 \] #### (d) \( g(z, x, y) \) \[ g(z, x, y) = \ln(z + x + y) \] Here, the function's form doesn't change; it is simply restructured. #### (e) \( g(x + h, y + k, z + l) \) \[ g(x + h, y + k, z + l) = \ln((x + h) + (y + k) + (z + l)) \] This simplifies to: \[ g(x + h, y + k, z + l) = \ln(x + y + z + h + k + l) \] Here, the inputs are expressed as summing each variable \(x, y, z\) with additional parameters \(h, k, l\). ### Notes - The natural logarithm function \(\ln\) is defined only for positive arguments. When evaluating these functions, ensure the sum \(x + y + z\) is positive; otherwise, the function does not exist (DNE). - Be mindful of the domain restrictions for the logarithmic function when calculating \( g(x, y, z) \). The function \( \ln(x + y + z
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