### Determining the Equation of the Tangent Line**Problem Statement:**Find the equation of the tangent line to the function \( y = x + \tan(x) \) at the point where \( x = \pi \).**Solution Outline:**To determine the equation of the tangent line to the given function at a specific point, we need to follow these steps:1. **Find the value of \( y \) at \( x = \pi \).**2. **Calculate the derivative of the function to determine the slope of the tangent line at \( x = \pi \).**3. **Use the point-slope form of the line equation to write the equation of the tangent line.****Step-by-Step Solution:**1. **Evaluate \( y \) at \( x = \pi \):** Given the function \( y = x + \tan(x) \): \[ y(\pi) = \pi + \tan(\pi) \] Since \(\tan(\pi) = 0\), we have: \[ y(\pi) = \pi + 0 = \pi \] Therefore, the point of tangency is \((\pi, \pi)\).2. **Calculate the derivative of \( y \):** The derivative \( y' \) of the function \( y = x + \tan(x) \) is: \[ \frac{dy}{dx} = 1 + \sec^2(x) \] At \( x = \pi \), we have: \[ \frac{dy}{dx} \bigg|_{x = \pi} = 1 + \sec^2(\pi) \] Since \(\sec(\pi) = -1\), \(\sec^2(\pi) = 1\), thus: \[ \frac{dy}{dx} \bigg|_{x = \pi} = 1 + 1 = 2 \] Therefore, the slope of the tangent line at \( x = \pi \) is \( 2 \).3. **Write the equation of the tangent line:** Using the point-slope form \( y - y_1 = m(x - x_1) \), where \( m \) is the slope and \((x_

Name: ### Determining the Equation of the Tangent Line**Problem Statement:*
Uploaded: 2024-03-20T06:46:42.000Z
Channel: Bartleby
Description: ### Determining the Equation of the Tangent Line**Problem Statement:**Find the equation of the tangent line to the function \( y = x + \tan(x) \) at the point where \( x = \pi \).**Solution Outline:**To determine the equation of the tangent line to