Purdue MA 166 Spring 2022 Exam 3 Question 1 (https://www.math.purdue.edu/php-scripts/courses/oldexams/serve_file.php?file=16600E3-S2022.pdf):

The answer is B (verified on desmos). How is this the case? Doesn't sin(3) approach sin(0) = 0 so the whole thing become 0 and E be the answer? Could someone explain?

D E Purdue N P Purdue U serv X P Purdue U Q ti 84 onli TI-84 GR Microsof serve_file Q how to e _ Limits In Q purdue n [Solved] + X https://www.math.purdue.edu/php-scripts/courses/oldexams/serve_file.p... Co G G . . . 4 of 15 Q + T V V MA 16600 Exam 3 , Page 2 of 13 Spring 2022 1. Compute the following limit: lim (2n)! sin 3 1 co n-too (2n - 1)! A. 2 B. 6 C. The limit does not exist. D. 3 E. 0 ENG 4:16 PM US 7/5/2022 4