The homework is worth 10 points. Show all of your work and put a box around your final answer. 1. Let f(2) = x- |2 - 11 Complete the following table of values. der 0.9 0.99 0.999 1.001 1.01 1.1 f(z) Use the table above to evaluate each of the following limits. rm (a) lim f(x), (b) lim f (ac) , x-+1- (c) lim f(x). (d) Use Desmos to sketch the graph. Does the graph confirm your answer? Explain. 2. Evaluate the limit assuming that lim f(x) = 3 and g(x) = 1. a) lim f(x)g(x) SEP 4 tv2. Evaluate the limit assuming that lim f(x) = 3 and g(x) = 1. (a) lim f(x)g(x) x-+ - 4 der (b) lim (2f (x) + 3g(x)) x- -4 (c) lim (f(x)) 3 x- -4 rm (d) lim 9(x) x--4 72 (e) lim f(2) + 1 x--492 -9 SEP 4 tv 4de 4+ 3 rm 1 - O -4 -3 -2 -1 3 A 5 ON -1- -2- -3- graph.png 3. From the above graph of y = f(x), find the following limits: (a) lim f(x) = (b) lim f(ac) = (c) lim f(x) = (d) lim f (ac) = x-+-4 x-+-3 SEP 4 tv 4Page of 3 ZOOM + orm graph.png 3. From the above graph of y = f(x), find the following limits: (a) lim f(x) = (b) lim f(x) = (d) lim f (x) = 20- -3 (c) lim f(x) = der (e) lim f (a) = (f) lim f(ac) = rm g) lim f(x) = (h) lim f (ac) = x-+4- x-+4 4. Let f(x) = 6 and g(x) = 4x + 1. Use the limit definition to verify the following limits: (a) lim f (x) = 6 x -+ 8 (b) lim g(x) = 17 x-+4 SEP 45. Find the limit, if it exists. If the limit does not exist, explain why. (a) lim Vx - 2 x 4 x2 - X de rm 1 (b lim x-+3+ 3 - X (c lim aC x-0 x SEP 4 tv 4