Problem 1) Let T (t) represent the unit tangent vector of 7(t) = < 1,t, t² >. A student is asked to calculate T '(0). The student starts by finding i '(t) =< 0,1,2t >. Plugging in t = 0, they find 7 '(0) =< 0,1,0 >. This is already a unit vector, so they conclude that T(0) =< 0,1,0 >. Finally, to find T '(0), they take the derivative of < 0,1,0 > component-wise. They conclude that T'(0) =< 0,0,0 >. The student's answer is incorrect. What mistake did the student make?

Calculus: Early Transcendentals
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Chapter1: Functions And Models
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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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Math 153
Concept Check 23
Problem 1) Let T (t) represent the unit tangent vector of 7(t) = < 1,t, t? >. A student is asked to
calculate T '(0).
The student starts by finding i '(t) =< 0,1,2t >. Plugging in t = 0, they find i '(0) =< 0,1,0 >. This is
already a unit vector, so they conclude that T'(0) =< 0,1,0 >.
Finally, to find T '(0), they take the derivative of < 0,1,0 > component-wise. They conclude that
T'(0) =< 0,0,0 >.
The student's answer is incorrect. What mistake did the student make?
Transcribed Image Text:Math 153 Concept Check 23 Problem 1) Let T (t) represent the unit tangent vector of 7(t) = < 1,t, t? >. A student is asked to calculate T '(0). The student starts by finding i '(t) =< 0,1,2t >. Plugging in t = 0, they find i '(0) =< 0,1,0 >. This is already a unit vector, so they conclude that T'(0) =< 0,1,0 >. Finally, to find T '(0), they take the derivative of < 0,1,0 > component-wise. They conclude that T'(0) =< 0,0,0 >. The student's answer is incorrect. What mistake did the student make?
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