Provide an appropriate response. Use the four step process to find f'(x) for the function f(x) = O_2h+x) x(x + h) O. 2(h+2x) x(x + h) O2(h+2x+xh) x(x + h) (h+2x) x(x + h) 2f(x)+ 3g(x) x-5 3f(x) Find the limit, if it exists. Given limf(x) = 4 and limg(x)= -5, find lim x-5 x-5 . 15 7271 15 Provide an appropriate response. Use a graphing utility to find the discontinuities of the given rational function. x+2x+1 f(x) = -1 1 3 x3+2x+5x-8 Continuous at all values of x Use - or where appropriate to describe the behavior at each zero of the denominator and identify all vertical asymptotes. x-16 f(x)= x+16 No zeros of denominator, no vertical asymptotes lim f(x)= lim f(x)=0; x = 0 is a vertical asymptote x-4- lim f(x)= x-4- lim f(x)=0; x-4- x-4+ lim f(x) = x; x = 4 is a vertical asymptote x-+ lim f(x)=0; x = -4 is a vertical asymptote Solve the problem. Suppose an object moves along the y-axis so that its location is y = f(x) = x + x at time x (y is in meters and x is in seconds). Find the average velocity (the average rate of change of y with respect to x) for x changing from 2 to 9 seconds. 12 m/s 84 m/s 15 m/s 3 m/s List the x-values in the graph at which the function is not differentiable. x=0 O x=-1 Ox=2 Ox=1 2 1 1 -2 20- Use the given graph to find the indicated limit. lim f(x) x-3- 0 3 2-