Answer to Question #184474 in Calculus for Njabulo

Question #184474

5. (Sections 6.1, 6.3) Consider the R − R 2 function r defined by r (t) = ￾ t, t2  ; t ∈ [−3, 3] . (a) Determine the vector derivative r 0 (1) by using Definition 6.1.1(b) Sketch the curve r together with the vector r 0 (1), in order to illustrate the geometric meaning of the vector derivative. Note: The curve r is the image of r, so it consists of all points (x, y) = (t, t2 ); t ∈ [−3, 3]


1
Expert's answer
2021-05-07T11:16:02-0400

"r(t)= (t,t^2)\\\\"


a)

"r'(t)=(1,2t)\\\\r'(1)=(1,2)"


b)

"(x,y)=(t,t^2)\\\\y=x^2\\ \\ \\ for\\ \\ \\ x\\in\\ (-3,3)\\\\"



"r'(1)=(1,2)\\\\"

This is tangent line at x=1, y=1 with slope m=2


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