3. Assume that f is uniformly continuous on a bounded set S, prove that f(S) is bounded. (hint: thm 19.4, 11.5) 4. Let ƒ(x) = (x-1)(x−3)² , ‚ determine limä→1 ƒ (x), limx→2 ƒ (x), limx→3 ƒ (x). (hint: limit may be infinite or does not exist).

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Q: 7. Intro To Real Analysis

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A: Definition of limit: Let be a function. If for every there exists such that and we can write it…

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A: The three criterias that you have mentioned are for a point. When we check the continuity at a…

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A: We need to show that the function does not have limit at point (0,0)

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A: Given limit: limx→-4 2x2+13x+20x+4

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A: To find out the limit.

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A: Given: limx→5x+11−4x−5

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A: The given limit is .The objective is to prove the limit does not exits.

Q: 23) lim f(x) x→1- f(x) 5- 4+ 3+ 2+ -5 -4 -3 -2 -1 -1. 5 х 2 4 -2+ -3+ -4+

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Q: 2ry? does not exist. now that the limit lim (z,y)+(0,0) x² + y!

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Q: 5. *Let I = (-∞, 2) U (2, +∞) and consider the following real-valued functions defined on I. x²-4 1…

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A: The answer provided below has been developed in a clear step by step manner.

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Q: 5) Compute the following limit if it exists 2 (x+y)³² - (x-g) ty lim (x,y)=(0,0) (012)

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A: See the solution below.

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A: Here,