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an IDH X a IDHS: Wc M Inbox (4) |M Ill y.JUl Bb *A data COXMod| Content 1037 X N Women's| Jer - Bing | chrome- corse her + X -> @ https://learn-us-east-1-prod-fleet01-xythos.content.blackboardcdn.com/blackboard.learn.xythos.prod/585304bab. G 53 1 of 1 + | Page view | A" Read aloud | V Draw Highlight Erase 1. Check if the following functions are continuous in their domain. (a) (6 points) f (x)= 2+2 for x 0 (b) (6 points) f ( x) = 1 for = 1 3. (18 points) Prove that each of the following equations has at least one solution in the given interval. (a) (6 points) x7 - 525 + 23 - 1 =0 in (-1, 1). (b) (6 points) 23 + 3x - 8 =0 in (-2, 3). (c) (6 points) Vr? + 1 = 3x in (0, 1). 4. (13 points) Let f be defined for all r E [-1, 1] by for r E (-1, 1) f (x) = 1 0 for = -1 and r = 1 (a) (5 points) Does f attain maximum and minimum values in [-1, 1]? (b) (8 points) Is f continuous for all r E [-1, 1]? 5. (10 points) Let f be defined for all r E (0, co) by f (2) = 1 *+1 for re (0, 1] for r E (1, 00) Prove that f attains maximum and minimum values. Verify that nevertheless none of the conditions in the extreme-value theorem is satisfied. 6. (1 point) How much did you spend on working on this assignment? Please provide the best estimate. Type here to search M 54OF Mostly cloudy 10:20 PM ENG 10/22/2021 28