Q1 [30pts]: Justify your answers clearly. Given the vector function - - ř(t) = (t² − 4t)i + sin(2t − 4)j + (½ + ½ )k a)

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Q1 30pts Justify Your Answers Clearly Given The Vector Function R T T 4t I Sin 2t 4 J K A 1 (50.24 KiB) Viewed 38 times

Q1 [30pts]: Justify your answers clearly. Given the vector function - - ř(t) = (t² − 4t)i + sin(2t − 4)j + (½ + ½ )k a) [10pts] Find the derivative of r(t). b) [10pts] Find the unit tangent vector of 7 (1) at t = 2. c) [10pts] Calculate F(t) dt. Q2 [30pts]: Justify your answers clearly. a) [10pts] Find and sketch the domain of the function f(x, y) = √4-x 1-x²-y² b) [10pts] Find the limit, if it exists, or show that the limit does not exist. 3x4 - 3y4 lim (x,y) (0,0) 2x² + 2y² c) [10pts] Given the function f(x, y) = e-3xy + sin² (5x) + ln(x² + y²) find all second derivatives.