A central concept in calculus is the extension of the tangent line to a circle to an arbitrary curve. In this exercise you will investigate finding the tangent line to a cirele using geometry and essentially using calculus. a. Find the equation of the tangent line to the unit circle at the point (1/2, v3/2) by finding the slope of the line that coincides with the ra- dius through the point as show in the figure below. b. The slope of a tangent line can also be computed using the difference quotient. - Write the upper half semi-circle as y = f(z) - Write the difference quotient for f(x) - Simplify the difference quotient using h(va+ vb) What happens to the simplified difference quotient as h → 0? Com- pare this result with what you found in part a.).

Calculus: Early Transcendentals
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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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A central concept in calculus is the extension of the tangent line to a circle
to an arbitrary curve. In this exercise you will investigate finding the tangent
line to a cirele using geometry and essentially using calculus.
a. Find the equation of the tangent line to the unit circle at the point
(1/2, v3/2) by finding the slope of the line that coincides with the ra-
dius through the point as show in the figure below.
b. The slope of a tangent line can also be computed using the difference
quotient.
- Write the upper half semi-circle as y = f(z)
- Write the difference quotient for f(x)
- Simplify the difference quotient using
h(va+ vb)
What happens to the simplified difference quotient as h → 0? Com-
pare this result with what you found in part a.).
Transcribed Image Text:A central concept in calculus is the extension of the tangent line to a circle to an arbitrary curve. In this exercise you will investigate finding the tangent line to a cirele using geometry and essentially using calculus. a. Find the equation of the tangent line to the unit circle at the point (1/2, v3/2) by finding the slope of the line that coincides with the ra- dius through the point as show in the figure below. b. The slope of a tangent line can also be computed using the difference quotient. - Write the upper half semi-circle as y = f(z) - Write the difference quotient for f(x) - Simplify the difference quotient using h(va+ vb) What happens to the simplified difference quotient as h → 0? Com- pare this result with what you found in part a.).
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