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(C) EXERCISES I. Evaluate the following limits. 1. lim (1+ Vw) (2- w2 + 3w3) w-+ 1 5. lim 4-3y2 -13 t2 - 1 V-+-2 6-y-32 2. lim x3 - 7x2 + 14x - 8 1--212 + 3t - 1 6. lim 2x2 - 3x - 4 2z + 22) 3 3. lim 2-+2 22 + 4 7. lim Vx2 +3 - 2 I-+-1 x2 +1 x2 - x-2 4. lim 8. lim V2x - V6 - x 0-+0 73 - 6x2 - 7x +1 C + 2 4 + x2 II. Complete the following tables. x - 5 x - 3 x2 - 6x + 9 r - 3 x2 - 6x +9 2.5 3.5 2.8 3.2 2.9 3.1 2.99 3.01 2.999 3.001 2.9999 3.0001 From the table, determine the following limits. 1. lim C - 5 4. lim x-3-x2 - 6x +9 2. lim x - 5. lim c-+3+ x2 - 6x +9 3. lim 1 3 x - 3 6. lim 1 3 x2 - 6x +9 III. Recall the graph of y = cscx. From the behavior of the graph of the cosecant function, determine if the following limits evaluate to too or to -co. 1. lim csc x 3. lim csci T-0- 2. lim csc x 4. lim cscx x-+0+ IV. Recall the graph of y = tan x. 1. Find the value of c E (0, 7) such that lim tan x = too. 2. Find the value of d E (7, 27) such that lim tana = -00