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Determine whether the following statements are true or false. Explain why or why not. 1. The curvature at a point depends on the speed at which a curve is traveled. 2. If f, g, and h are odd, integrable functions, and a is a real number then I (re)i + g(+)j +h(t)E) dt = 3. The functions F(t) = (cos t, sin t) and R(t) = (cos(t²), sin(t²)) generate the same set of (x, y, z) coordinates.

Determine whether the following statements are true or false. Explain why or why not. 1. The curvature at a point depends on the speed at which a curve is traveled. 2. If f, g, and h are odd, integrable functions, and a is a real number then I (re)i + g(+)j +h(t)E) dt = 3. The functions F(t) = (cos t, sin t) and R(t) = (cos(t²), sin(t²)) generate the same set of (x, y, z) coordinates.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 20T
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Determine whether the following statements are true or false. Explain why or why not. (See photo)

Determine whether the following statements are true or false. Explain why or why not. 1. The curvature at a point depends on the speed at which a curve is traveled. 2. If f, g, and h are odd, integrable functions, and a is a real number then pa I (()i+ g(t)j+ h(t)k) dt = ő 3. The functions 7(t) = (cos t, sin t) and R(t) = (cos(t²), sin(t²)) generate the same set of (x, y, z) coordinates.
Transcribed Image Text:Determine whether the following statements are true or false. Explain why or why not. 1. The curvature at a point depends on the speed at which a curve is traveled. 2. If f, g, and h are odd, integrable functions, and a is a real number then pa I (()i+ g(t)j+ h(t)k) dt = ő 3. The functions 7(t) = (cos t, sin t) and R(t) = (cos(t²), sin(t²)) generate the same set of (x, y, z) coordinates.
Expert Solution
Step 1

determine whether the following statements are true or false. explain why or why not .

1) the curvature at a point depends on the speed at which a curve is traveled.

it is known that curvature at a point r→t is defined as 

κt=T'→tr't

that is,

curvature is the length of acceleration vector if r→t traces the curve with constant speed 1.

implies, the statement is false since curvature does not depend on any parametrization.

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