Let 6. x1. Graph the function, and evaluate the following. (a) lim f(a) = (b) lim f(ac) = x-1+ (c) f(1) Note: Input DNE, infinity, and -infinity for does not exist, oo, and -oo, respectively.if x 2 Graph the function and evaluate the following. (a) lim h(a) = (b) lim h(ac) = x-+0 (c) lim h(x) = x-+1 (d) lim h(a) = (e) lim h(a) = (f) lim h(a) = Note: Input DNE, infinity, and -infinity for does not exist, oo, and -oo, respectively.Let (-5+ x, if x 3 (a) Evaluate each of the following. (i) lim f(x) = (ii) lim f (ac) = x-3+ (ifi) f (3) = (b) Is the function f (x) continuous at x = 3? ? V Note: Input DNE, infinity, and -infinity for does not exist, co, and -oo, respectively.If a ball is thrown straight up into the air with an initial velocity of 75 ft/s, its height in feet after t seconds is given by 2 y 2 75:5 161,L . (a) Find the average velocity (using 3 decimal places if necessary) for the time period beginning when t : 2 and lasting (i) 0.1 seconds. Answer: ft/s (ii) 0.01 seconds. Answer: ft/s (iii) 0.001 seconds. Answer: We (b) Based on the above results, guess what the instantaneous velocity of the ball is when t : 2. Answer: We Suppose that f (m) : 8m2 + 322. Use the limit definition of the derivative to find: (a) The slope of the line tangent to f(:13) at m = 2. Answer: (b) The instantaneous rate of change of an) at m : 2. Answer: (6) The equation of the line tangent to f(:l':) at :1: = 2. Answer: 3; =