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o(e) = La t -Va V1 + t²

o(e) = La t -Va V1 + t²

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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The equation presented is: \[ c) \, g(x) = \int_{-\sqrt{x}}^{x} \frac{t}{\sqrt[3]{1 + t^2}} \, dt \] This equation represents a definite integral of the function \(\frac{t}{\sqrt[3]{1 + t^2}}\) with respect to \(t\), evaluated from the lower limit \(-\sqrt{x}\) to the upper limit \(x\). In this context: - \(g(x)\) is the integral function of \(x\). - The numerator \(t\) signifies the variable of integration. - The denominator is the cube root of \(1 + t^2\), which affects the rate of change of the integrand within the integral's bounds.
Transcribed Image Text:The equation presented is: \[ c) \, g(x) = \int_{-\sqrt{x}}^{x} \frac{t}{\sqrt[3]{1 + t^2}} \, dt \] This equation represents a definite integral of the function \(\frac{t}{\sqrt[3]{1 + t^2}}\) with respect to \(t\), evaluated from the lower limit \(-\sqrt{x}\) to the upper limit \(x\). In this context: - \(g(x)\) is the integral function of \(x\). - The numerator \(t\) signifies the variable of integration. - The denominator is the cube root of \(1 + t^2\), which affects the rate of change of the integrand within the integral's bounds.
4. Differentiate a) \( g(x) = \int_{0}^{x} \cos(t^2) \, dt \)
Transcribed Image Text:4. Differentiate a) \( g(x) = \int_{0}^{x} \cos(t^2) \, dt \)
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