1. [13.2 & 13.3: Calculus on Curves] Let C be the curve parametrized by r(t): 2ti...

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1. [13.2 & 13.3: Calculus on Curves] Let C be the curve parametrized by r(t): √2ti + e¹j + etk for 1 ≤ t ≤ 1. (a) Find the velocity vector at t = 0. (b) Find the acceleration vector at t = 0. (c) Parametrize the tangent line to C at t = 0. (d) Calculate the length of C. Hint: Show that the formula for the speed of the curve is the square root of a perfect square. = 2. [14.1: Functions of Several Variables] Sketch the level curves f(x, y) = c of the following functions z = f(x, y) at the specified values of c. (a) f(x,y) 1 1+x²+4y²¹ c = 1, 2, 4. (b) f(x,y) exp(x2 - y2), c = 1, 2, 3. (c) f(x,y) = y sinx, c = 0, +1, +2. (d) f(x,y) = = = 1 + xy², c = 0, ±1. Hint: Solve f(x, y) = c for x in terms of y and c. 1. [13.2 & 13.3: Calculus on Curves] Let C be the curve parametrized by r(t): √2ti + e¹j + etk for 1 ≤ t ≤ 1. (a) Find the velocity vector at t = 0. (b) Find the acceleration vector at t = 0. (c) Parametrize the tangent line to C at t = 0. (d) Calculate the length of C. Hint: Show that the formula for the speed of the curve is the square root of a perfect square. = 2. [14.1: Functions of Several Variables] Sketch the level curves f(x, y) = c of the following functions z = f(x, y) at the specified values of c. (a) f(x,y) 1 1+x²+4y²¹ c = 1, 2, 4. (b) f(x,y) exp(x2 - y2), c = 1, 2, 3. (c) f(x,y) = y sinx, c = 0, +1, +2. (d) f(x,y) = = = 1 + xy², c = 0, ±1. Hint: Solve f(x, y) = c for x in terms of y and c.