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.).

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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Mathematics For Machine Technology

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ISBN:9781337798310

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Publisher:Peterson, John.

Chapter67: Analysis Of Trigonometric Functions

Section: Chapter Questions

Problem 11A: Refer to the following figure in answering Exercises 7 through 13. It may be helpful to sketch...

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this is one question

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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Step 1: Part-a (Slope of the tangent line)

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Step 2: Part-a (Equation of the tangent line)

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Step 3: Part-b (Equation of upper half of semicircle)

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Step 4: Part-b (Difference quotient)

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Step 5: Part-b (Simplify the difference quotient)

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Step 6: Part-b (when h tends to 0)

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Step 7: Part-b (value of simplified difference quotient at x=1/2)

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