Lesson 13 Problem Set 5.1 Answer Key: Introduction and Explanation
In mathematics, problem sets are an essential part of the learning process. They allow students to practice applying concepts and techniques learned in class to solve various mathematical problems. Lesson 13 Problem Set 5.1 is one such exercise that focuses on specific topics covered in the lesson. This article serves as an answer key to help students understand the solutions and justifications behind each problem.
Lesson 13 Problem Set 5.1 Answer Key: Detailed Solutions and Justifications
This section provides detailed solutions and justifications for Lesson 13 Problem Set 5.1. Each problem is analyzed and explained step by step, ensuring a clear understanding of the concepts and techniques involved.
Problem: Find the derivative of the function f(x) = 3x^2 + 2x – 1.
Solution: To find the derivative of the function, we need to apply the power rule of differentiation. Taking the derivative term by term, we get f'(x) = 6x + 2. The derivative represents the rate of change of the function at any given point.
Problem: Solve the equation 2x^2 + 5x – 3 = 0.
Solution: To solve the equation, we can use the quadratic formula. Plugging in the values from the given equation into the formula, we get x = (-5 ± √(5^2 – 4(2)(-3))) / (2(2)). Simplifying further, we have x = (-5 ± √49) / 4. This leads to two solutions: x = (-5 + 7) / 4 = 1/2 and x = (-5 – 7) / 4 = -3.
Problem: Evaluate the integral ∫(4x^3 + 2x^2 – 5x + 7) dx.
Solution: To find the integral of the given function, we apply the power rule of integration. Taking the integral term by term, we get (4/4)x^4 + (2/3)x^3 – (5/2)x^2 + 7x + C. Simplifying further, we have x^4 + (2/3)x^3 – (5/2)x^2 + 7x + C, where C represents the constant of integration.
In conclusion, this article has provided the answer key for Lesson 13 Problem Set 5.1. By delving into the detailed solutions and justifications for each problem, students can gain a comprehensive understanding of the concepts and techniques involved. It is essential to remember that mathematics requires practice and continuous learning to strengthen problem-solving skills.