Find the tangent line to the graph the eq uati on of of YCK)- %3D at X=0 11-x2

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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**Finding the Tangent Line to a Curve**

**Problem Statement:**

Find the equation of the tangent line to the graph of 

\[ Y(x) = \frac{4x}{\sqrt{1-x^2}} \]

at \( x = 0 \).

**Solution:**
The goal is to determine the equation of the tangent line at the specified point. 

**Equation of Tangent Line:**

\[ y = \underline{\hspace{4cm}} \] (This space is typically for the calculated equation of the tangent line after solving the problem).

To find this equation:
1. Determine \( Y(x) \) and the derivative \( Y'(x) \).
2. Evaluate \( Y'(x) \) at \( x = 0 \) to find the slope of the tangent line.
3. Use the point-slope form of the line equation to determine the final equation of the tangent.

The equation remains incomplete and is to be filled in after calculations.
Transcribed Image Text:**Finding the Tangent Line to a Curve** **Problem Statement:** Find the equation of the tangent line to the graph of \[ Y(x) = \frac{4x}{\sqrt{1-x^2}} \] at \( x = 0 \). **Solution:** The goal is to determine the equation of the tangent line at the specified point. **Equation of Tangent Line:** \[ y = \underline{\hspace{4cm}} \] (This space is typically for the calculated equation of the tangent line after solving the problem). To find this equation: 1. Determine \( Y(x) \) and the derivative \( Y'(x) \). 2. Evaluate \( Y'(x) \) at \( x = 0 \) to find the slope of the tangent line. 3. Use the point-slope form of the line equation to determine the final equation of the tangent. The equation remains incomplete and is to be filled in after calculations.
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