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find the curvature k of the curve at the point p. r(t) = et cos(t)i + et sin(t)j + etk, p(1, 0, 1).

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Keith Leannon
Keith LeannonLv2
17 Apr 2020

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5. Do the following tasks using Mathematica

    For a Parametric curve  χ =  χ (t) , y = y(t) the curvature at a point p is:

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       Hint: At top of any one of it's arches y is maximum 

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    For a Parametric curve  χ =  χ (t) , y = y(t) the curvature at a point p is:

Problem 4 Circle your answer. a) (6 points) If f(x) = 2x + 3x2 - 361 + 5, then the tangent line to the graph y= f(x) is horizontal when i) 1 = -2,3 ii) I = 2,-3 iii) r = 0 iv) not listed b) [6 points] Suppose Given h(x) = f(g(T)), where g(2) = 3, g'(2) = 7, f'(2) = -1 and 1'(3) = -2. Then h'(2) is equal to i) - 1 ii) -2 iii) - 14 iv) not listed (x+3)(1 - 1)3 c) (6 points) The function f(1) == (x2 - 2x + 1)(x + 3) wa has vertical asymptotes at i) x = -3,0 ii) = -3,0,1 iii) x = 0,1 iv) not listed d) (6 points] The solution to the initial value problem v'(x) = 473 – cos(x) +e", y(0) = 3 is i) y(x) = x + sin(x) + e* + 2 ii) y(I) = x4 – sin(x) +et+2 iii) y(x) = 2* – sin(1) + et + 3 iv) not listed

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