1.2 Problems 1. Use the functions f and g defined by the graphs below to determine the following limits. (a) lim If (x) + 8(x)] f (x) x - 1 (c) lim x-1g(x) (b) lim f(x) . 8(x) x-+1 (d) lim f((8(x)) x 1 y g(x) 2 y f(x) 2 N N7. Use the graph below to estimate the values of these limits. (It helps to recognize what the limit represents.) (a) lim f(0 + h) -f(0) (d) lim f (3 + h) - f(3) h +0 h h-0 (b) lim f(1 + h) - f(1) (e) lim f ( 4 + 1 ) - f ( 4 ) h h-0 (c) lim f (2 + w) - 1 (f) lim f ( 5 + s ) - f ( 5 ) W +0 w S 3- i y=f(x) w A264 DERIVATIVES AND GRAPHS 11. You have been asked to determine where a wa- ter works should be built along a river between Chesterville and Denton (see below) to minimize the total cost of the pipe to the towns. D pipe pipe 5 river X 10 (a) Assume that the same size (and cost) pipe is used to each town. (This part can be done quickly without using calculus.) (b) Assume instead that the pipe to Chesterville costs $3000 per mile and to Denton it costs $7000 per mile.PROBLEMS In problems 1 , rewrite the limit of each Riemann sum as a definite integral. n 1. lim (2+ 30 )AX * on the interval [ 0, 4] mesh-0 k=15. Use the graphs shown below and the function h(x) - x 2 to determine the values of (a) f (f(1)). f (8(2)), f (8(0)), f (8(1)) (b) 8 (f(2)), 8 (f(3)), 8 (8(0)), 8 (f(0)) (c) f (h(3)), f (h(4) ), h (g(0)), h (g(1)) 2 yag (x) y=f(x) X 2 W 2 w3.1 Problems 1. Label all of the local maximums and minimums of the function in the figure below. Also label all of the critical points. 10