Question

10. Consider the behavior of values of sin near x = 0. The graph of X 1 sin shown to the right. Answer parts (a), (b), and (c) WAS 0 5 -1 (a) Create a table of values of sin xl- for the following values of x. Complete the following table. 2 2 2 311 2 5.0 2 7 х 2 11x it 91 sin Describe the pattern of values that can be observed in the table. Choose the correct answer below. O A. The value of sin (4 ) approaches (Type an integer or a fraction.) X OB. The value of sin is constant O C. The value alternates between 1 and -1 :) near x=0? Choose the correct answer (b) Why does a graphing utility have difficulty plotting the graph of y = sin below. O A. The function sin ) is not defined near x = 0 B. The alternation between 1 and -1 happens infinitely many times on the interval (0. h) no matter how small h> 0 becomes OC. The function sin ( tends to co near x=0. (c) What do you conclude about lim sin (hech ? Choose the correct answer below (Type an integer or a fraction.) O Alim sin x0 (3)- (1) OB, lim sin does not exist x 1

Answer 1

(a). To Create table for sin (): 2 2 e 2 ST 2 512 2 AR IL sin D an 1 11 TL 1 1 1 - 1 So option С The valve alternates between (6) The graphing unility have difficulty plotting the graph of y y = sin ( 1 ) near 20 B) The alternation between 1 & I happers m the interval (oh) no matter how small hyo becomes. many times on (c) lime sin () = ? B lim lim sin ( 1 ) does does not exist. Ž0 Hope this is helppul!