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MATH 2413
Oct 25, 2023
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D:ego ES? yNoTon Brendan Caseria MATH 2413: Dallas College Due: 9/10/2023 Homework 3: 2.4, 2.5 Question 1. Compute the following limits. " 2 a) lim e S Hint: Careful with the square root! T-2" \/;2--]- r2—-6 Xy 2 (xx2) l 1. —— e Jir el X T=X=b = CXFL) [X-3) , " 2 r__( T & S 5 Ty 5 A b) zl_igl+ arctan(In(x)) Hint: Individual graphs of In(z) and arctan(z) might help here. ae) = UNACTiacd 51 X~o" »\a=0 AN - atcran(-=) = Scanned with CamScannér
2 Question 2. Carefully consider the following statements. Either prove them using the Intermediate Value Theorem or explain why IVT does not apply. a) In 1962, Wilt Chamberlain scored 100 points in a basketball game using only 1-point and 2-point baskets. At some point during the game, he had scored 32 points. v doesnck | aggly - beose relsonsio bexwesn X ond 4 aly s ad cofelared b) In 2002, Mike Crean hit a golf ball 517 yards directly into the hole for a "hole-in-one", the longest such shot ever recorded. At some point in its flight, the ball was exactly 314 yards from the hole. Scanned with CamScanner
Question 3. Using the definition of continuity, find the (a,b) pair such that the following furiction 15 continuous for all z. 2bx +4a, <1 -\0 f(z)={b—3a, r=1-\0 1822 +4b, £>1-\0 Fa-C A0 2;":':\ Zbxa b 34 Faxk =0 ta-LE0 "IAN _ ¢ Yo b-3s 21k -A S0 N 2y bbb i (- W 3813 g b=.C-0 B -3 Conriniovs bpegause ¥NE ol moreh O hen o= 1, ond b Z —Te Scanned with CamScanner
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