Lesson 14 HW 5.2 Answer Key: Uncover the Solutions
Homework assignments can sometimes be challenging, leaving students feeling frustrated and uncertain about their answers. However, with the Lesson 14 HW 5.2 Answer Key, students can now have a sigh of relief. This article aims to provide clarity and guidance by presenting the solutions to Lesson 14 Homework 5.2 problems. Dive into this article to uncover the answers and gain a better understanding of the concepts covered in this assignment.
Dive into Lesson 14 HW 5.2: Get Clarity with the Answer Key
Problem 1: Find the derivative of the function f(x) = 3x^2 + 2x – 5. To find the derivative, we need to apply the power rule for derivatives. The power rule states that for a function of the form f(x) = ax^n, the derivative is given by f'(x) = anx^(n-1). Applying this rule to our function, we obtain f'(x) = 6x + 2.
Problem 2: Evaluate the integral ∫(4x^3 – 2x^2 + 5x – 3)dx. To evaluate this integral, we need to apply the power rule for integration. The power rule states that for a function of the form f(x) = ax^n, the integral is given by ∫f(x)dx = (a/(n+1))x^(n+1) + C, where C is the constant of integration. Applying this rule to our integral, we obtain ∫(4x^3 – 2x^2 + 5x – 3)dx = (4/4)x^4 – (2/3)x^3 + (5/2)x^2 – 3x + C.
Problem 3: Solve the differential equation dy/dx = 2x + 3. To solve this differential equation, we need to integrate both sides with respect to x. Integrating the left side gives us ∫dy = y + C1, where C1 is the constant of integration. Integrating the right side gives us ∫(2x + 3)dx = x^2 + 3x + C2, where C2 is another constant of integration. Therefore, the solution to the differential equation is y = x^2 + 3x + C.
Clarity Achieved with the Lesson 14 HW 5.2 Answer Key
With the Lesson 14 HW 5.2 Answer Key at hand, students can now confidently tackle their homework problems. By providing the solutions to problems involving derivatives, integrals, and differential equations, this article aims to help students gain a better understanding of these concepts. Remember, practice makes perfect, so make sure to review these answers and attempt similar problems to solidify your understanding.