**Mathematics Problem Transcription** --- ### Problem 1: \[ 3x^2 \sqrt{x^2 - 36} + x^3 \cdot \frac{1}{2} (x^2 - 36)^{-1/2} \cdot 2x = \] ### Problem 2: \[ 3x^2 (x^2 - 36) + x^4 \] \[ \sqrt{x^2 - 36} \] --- **Detailed Description:** 1. **Problem 1:** This equation combines polynomial and radical expressions. It consists of a term with a square root, product of polynomials, and a product of fractional exponents: - The first term is \(3x^2 \sqrt{x^2 - 36}\). - The second term involves several components: \( x^3 \), the fraction \(\frac{1}{2}\), the radical \((x^2 - 36)^{-1/2}\) raised to a negative fractional exponent, and multiplied by \( 2x \). 2. **Problem 2:** This problem is an entirely different expression written methodically: - The numerator is composed of two terms: \( 3x^2 (x^2 - 36) \) and \( x^4 \). - The denominator is a square root: \( \sqrt{x^2 - 36} \). Given the algebraic complexity, these problems likely pertain to calculus or pre-calculus topics for high school or university-level coursework, focusing on polynomial and radical expressions.

Mathematics Problem Transcription --- ### Problem 1: \[ 3x^2 \sqrt{x^2 - 36} + x^3 \cdot \frac{1}{2} (x^2 - 36)^{-1/2} \cdot 2x = \] ### Problem 2: \[ 3x^2 (x^2 - 36) + x^4 \] \[ \sqrt{x^2 - 36} \] --- Detailed Description: 1. Problem 1: This equation combines polynomial and radical expressions. It consists of a term with a square root, product of polynomials, and a product of fractional exponents: - The first term is \(3x^2 \sqrt{x^2 - 36}\). - The second term involves several components: \( x^3 \), the fraction \(\frac{1}{2}\), the radical \((x^2 - 36)^{-1/2}\) raised to a negative fractional exponent, and multiplied by \( 2x \). 2. Problem 2: This problem is an entirely different expression written methodically: - The numerator is composed of two terms: \( 3x^2 (x^2 - 36) \) and \( x^4 \). - The denominator is a square root: \( \sqrt{x^2 - 36} \). Given the algebraic complexity, these problems likely pertain to calculus or pre-calculus topics for high school or university-level coursework, focusing on polynomial and radical expressions.

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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