Question 1 Mark this question Determine if the conditions of the mean value theorem are met by the function f(x)=x-2x on [1, 3]. If so, find the values of c in (1, 3) guaranteed by the theorem. f(x) is a polynomial and therefore is continuous on [1, 3] and differentiable on the interval (1, 3). The value guaranteed by the mean value theorem is c = 2. f(x) is a polynomial and therefore is continuous on [1, 3] and differentiable on the interval (1, 3). The value guaranteed by the mean value theorem is c = 39 3 f(x) is a polynomial and therefore is continuous on [1, 3] and differentiable on the interval (1, 3). The value guaranteed by the mean value theorem is c = 2. f(x) is a polynomial and therefore is continuous on [1, 3] and differentiable on the interval (1, 3). 39 The value guaranteed by the mean value theorem is c = 3 So 7 v(t)dt = 10 miles; the boat is 10 miles away from shore at 7 PM. - v(t)dt 10 miles; the boat is 10 miles away from shore at 7 PM. 7 Ov(t)dt = 22 miles; the boat is 22 miles away from shore at 7 PM. 0 7 v(t)dt = 12 miles; the boat is 12 miles away from shore at 7 PM. Question 2 Mark this question Consider the graph below, which represents the velocity v(t) of a rowboat moving away from its starting point onshore at 12 PM (t = 0). A positive velocity indicates straight-line motion away from shore; while a negative velocity indicates straight-line motion back toward shore. Use the graph to find 1 (t) dt and determine the position of the boat relative to shore at 7 pm. Velocity (Miles/Hour) 0 -1 -2 -3 -4 2 + y 4 3 2 3 4 5 6 7 Time (In Hours) Question 3 Given lim f(x) = -56 and lim g(x) = -4, evaluate lim x 8 X-8 18-x f(x) lim X - = 6 lim 8L f(x) -3=11 lim x f(x) [53]=17 g(x) -3 f(x) lim X g(x) -] = -11 17 f(x) g(x) Graph the following function: 3 f(x)= 21 6 4 3 1 -6 -5 -4 -3 -2 -1 0 1 2 3 4 -2 10 5 6 60 9 . 4 3 -1 -6 -5 -4 -3 -2 0 1 2 3 4 5 N 60 -4 -5 6 O y 60 5 4 3 1 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 x -1 -2 -4 -5 -6