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Final Worksheet November 29, 2017 I. (5 pts) The formula limå®0 sin(θ)/θ = i can be generalized. If lin-o f(z) = 0 and f(z) is never zero in an open interval containingthe point -e, expect possible at etsel, then lim sin((a)) sin(f(z))-1. - f(x) Use this theorem to find the limit of sin r) lim Justify your use of the theorem. 2. (5 pts) The coordinates of a particle moving in the metric zy-plane are differentiable fund tions of time t with dr/dt = 10m/sec and dy/dt-5m/sec. How fast is the particle movin away from the origin as it passes through the point (3,-4)? 3, (5 pts) Two sides of a triangle have lengths a and b, and the angle between them is θ. Wh value of θ will maximize the triangle's area? Hint: A = (1/2)absin(0). 4. (5 pts) Show that y r2 + / -dt solves the initial value problem 5. BONUS: (5 pts) At points on a circle of radius a, line segments are drawn perpendicular the plane of the circle. Each perpendicular line segment at point P on the circle has leng ks, where s is the length of the arc of the circle measured counterclockwise from (a, 0) P and k is a positive constant. Find the area of the surface formed by the perpendicular I segments along the arc beginning at (a, 0) and extending once around the circle.