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Consider the space curve C given by the vector function f(t) = (t² + 1)i + (2t4 – 3t2)j +t³k where t e [-1,2]. Í(t) %3D (a) By inspection, state and give a brief reason in words, whether or not C is smooth. (b) By inspection, state and give a brief reason in words, whether or not the tangent line to C at the point (1,0,0) exists. (You may use normal print f or “the vector function" and f' or “the derivative" for f and f' respectively in typing up your brief response when referring to the function and its derivative, respectively. Give statements like, for example “The r-component of f is not continuous", or “The z-component of the deriva- tive is not zero when t = 0", etc. You are not required to type in the actual %3D algebraic expression.)

Consider the space curve C given by the vector function f(t) = (t² + 1)i + (2t4 – 3t2)j +t³k where t e [-1,2]. Í(t) %3D (a) By inspection, state and give a brief reason in words, whether or not C is smooth. (b) By inspection, state and give a brief reason in words, whether or not the tangent line to C at the point (1,0,0) exists. (You may use normal print f or “the vector function" and f' or “the derivative" for f and f' respectively in typing up your brief response when referring to the function and its derivative, respectively. Give statements like, for example “The r-component of f is not continuous", or “The z-component of the deriva- tive is not zero when t = 0", etc. You are not required to type in the actual %3D algebraic expression.)

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 18T
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Consider the space curve C given by the vector function f(t) = (t² + 1)i + (2t4 – 3t2)j + t³k where t e [-1,2]. (a) By inspection, state and give a brief reason in words, whether or not C is smooth. (b) By inspection, state and give a brief reason in words, whether or not the tangent line to C at the point (1,0,0) exists. (You may use normal print f or “the vector function" and f' or “the derivative" for f and f' respectively in typing up your brief response when referring to the function and its derivative, respectively. Give statements like, for example "The r-component of f is not continuous", or “The z-component of the deriva- tive is not zero when t = 0", etc. You are not required to type in the actual algebraic expression.)
Transcribed Image Text:Consider the space curve C given by the vector function f(t) = (t² + 1)i + (2t4 – 3t2)j + t³k where t e [-1,2]. (a) By inspection, state and give a brief reason in words, whether or not C is smooth. (b) By inspection, state and give a brief reason in words, whether or not the tangent line to C at the point (1,0,0) exists. (You may use normal print f or “the vector function" and f' or “the derivative" for f and f' respectively in typing up your brief response when referring to the function and its derivative, respectively. Give statements like, for example "The r-component of f is not continuous", or “The z-component of the deriva- tive is not zero when t = 0", etc. You are not required to type in the actual algebraic expression.)
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