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(a) f(0) = ln(sin 0) + sin(ln €). (c) y = ln |x³ — x²| (b) f(x) = log₁0(1 + cos x) ax In (a + x) (d) G(x) = In

(a) f(0) = ln(sin 0) + sin(ln €). (c) y = ln |x³ — x²| (b) f(x) = log₁0(1 + cos x) ax In (a + x) (d) G(x) = In

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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find the derivitive of each function please

This page presents a series of mathematical functions for educational purposes: (a) The function \( f(\theta) = \ln(\sin \theta) + \sin(\ln \theta) \). This function combines the natural logarithm and sine functions with the variable \(\theta\). (b) The function \( f(x) = \log_{10}(1 + \cos x) \). Here, the logarithm to base 10 is applied to the expression \(1 + \cos x\). (c) The function \( y = \ln |x^3 - x^2| \). This involves the natural logarithm of the absolute value of the expression \(x^3 - x^2\). (d) The function \( G(x) = \ln \left(\frac{a - x}{a + x}\right) \). It takes the natural logarithm of the fraction \(\frac{a - x}{a + x}\), where \(a\) is a constant. (e) The function \( y = x^2 \ln[\ln x] \). This involves multiplying \(x^2\) by the natural logarithm of the natural logarithm of \(x\). These functions illustrate the use of logarithmic and trigonometric operations in mathematical expressions.
Transcribed Image Text:This page presents a series of mathematical functions for educational purposes: (a) The function \( f(\theta) = \ln(\sin \theta) + \sin(\ln \theta) \). This function combines the natural logarithm and sine functions with the variable \(\theta\). (b) The function \( f(x) = \log_{10}(1 + \cos x) \). Here, the logarithm to base 10 is applied to the expression \(1 + \cos x\). (c) The function \( y = \ln |x^3 - x^2| \). This involves the natural logarithm of the absolute value of the expression \(x^3 - x^2\). (d) The function \( G(x) = \ln \left(\frac{a - x}{a + x}\right) \). It takes the natural logarithm of the fraction \(\frac{a - x}{a + x}\), where \(a\) is a constant. (e) The function \( y = x^2 \ln[\ln x] \). This involves multiplying \(x^2\) by the natural logarithm of the natural logarithm of \(x\). These functions illustrate the use of logarithmic and trigonometric operations in mathematical expressions.
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