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Calculus
4x2. + 9y2 - 36 (v3.)

4x2. + 9y2 - 36 (v3.)

Calculus: Early Transcendentals
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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Find the slope of the graph at the given point.

The image displays a graph featuring an ellipse and a line. **Equation of the ellipse:** The ellipse is represented by the equation \(4x^2 + 9y^2 = 36\). 1. **Ellipse Description:** - The ellipse is centered at the origin (0,0). - It is elongated horizontally along the x-axis. - The axes of the ellipse intersect at the origin. 2. **Axes and Scale:** - Both the x-axis and y-axis are displayed, helping to illustrate the position and scale of the ellipse. Units are marked on each axis for reference. 3. **Tangent Line:** - A red line is drawn tangent to the ellipse. This tangent line visually represents the point of tangency on the ellipse. 4. **Point of Tangency:** - The point where the tangent touches the ellipse is marked by the coordinates \((\sqrt{5}, \frac{4}{3})\), indicating the precise location on the graph. This graph is an example of analyzing the interaction between ellipses and tangent lines, highlighting the geometric relationships and calculations involved in analytical geometry.
Transcribed Image Text:The image displays a graph featuring an ellipse and a line. **Equation of the ellipse:** The ellipse is represented by the equation \(4x^2 + 9y^2 = 36\). 1. **Ellipse Description:** - The ellipse is centered at the origin (0,0). - It is elongated horizontally along the x-axis. - The axes of the ellipse intersect at the origin. 2. **Axes and Scale:** - Both the x-axis and y-axis are displayed, helping to illustrate the position and scale of the ellipse. Units are marked on each axis for reference. 3. **Tangent Line:** - A red line is drawn tangent to the ellipse. This tangent line visually represents the point of tangency on the ellipse. 4. **Point of Tangency:** - The point where the tangent touches the ellipse is marked by the coordinates \((\sqrt{5}, \frac{4}{3})\), indicating the precise location on the graph. This graph is an example of analyzing the interaction between ellipses and tangent lines, highlighting the geometric relationships and calculations involved in analytical geometry.
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