Question

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a. Let C be the curve which is represented by the vector valued function r(t) = xi + /2; +*+?k, Osts 2. Find the arc length of C. b. Let C be the curve with parametric equation x = 2t? and y = 8+9+ t, then find the equation of the tangent line to the curve C corresponding to the point t = 1.

Answer 1

Solution: 03132 The length for a curve in space with a vector equation r(t)=1 (1),g(t);h(0), a stsbis aytiren Me)= (43440 given by the formula L=L*12*42)* +(2°C)* +(2()'d Here 11e)= (4.2014)=r(e)=(0,3,4) Novu -fev -(3) - C5 ****** *** B)Given r(t) = (2x3, 82 + c) t=1 = -(1) = {(1)98(1)+(1)= (1,9) = ='(t)=(4,244)= ''(1)= (4(1),24 (1))= {4,24) So the parametric equations for the tangent line at t = 1 to the curve is: (x,y,z)=r(1) +(r'(1)) :. Tangent line is : (x,y)= (1,9)+ (4,24) : Z) = (1+41,9+241)