3.5: #10a, #16, #30a 10. You have been asked to determine the least expensive route for a telephone cable that connects Andersonville with Beantown (see figure below). (a) If it costs $5000 per mile to lay the cable on land and $8000 per mile to lay the cable across the river (with the cost of the cable included), find the least expensive route. (b) What is the least expensive route if the cable costs $7000 per mile in addition to the cost to lay it? 16. Find the shortest distance from the point (2, 0) to the curve: (a) y = 3x - 1 (b) y = x 2 (c) x 2 + y 2 = 1 (d) y = sin(x) 30. (a) Find the dimensions of the rectangle with the greatest area that can be built so the base of the rectangle is on the xaxis between 0 and 1 and one corner of the rectangle is on the curve y = x 3 . What is the area of this rectangle? Section 3.6: #6, #16, #44, #56 For problems 4 - 24, calculate the limit of each expression as "x ." 7 x +12 6. 3 x2 16. x+sin ( x) xsin(x) In problems 42 - 50, write the equation of each asymptote for each function and state whether it is a vertical or horizontal asymptote x1 f ( x )= 2 44. x x In problems 51 - 59, write the equation of each asymptote for each function. x 2 f ( x )=x + 56. x +1 Section 3.7: #8, #22, #18 Determine the limits in problems 1 - 15. 8. lim x ln (x) x Determine the limits in problems 21 - 29. 3 x lim x e 22. x 18. 3 x +5 has the indeterminate form / . Why doesn't l'H^o x 2 x1 lim pital's Rule work with this limit? (Hint: Apply l'H^ o pital's Rule twice and see what happens.) Evaluate the limit without using l'H^ o pital's Rule