Exercise 3. T = Suppose X is an infinite set equipped with the cofinite topology = {U C X | X \ U finite} U {0}. Show that every continuous function ƒ : X → C is constant (here C is equipped with the usual topology 7.).

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A: Note: As per our guidelines, we can solve the first question. Please repost the remaining questions.

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A: Answer:  a=8b=−3c=−2−r2−10rExplanation:Step 1:

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Q: Good afternoon, Unsure how to approach this.

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A: We have to find the solution of the exact differential equation .

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A: The given differential equation

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A: a=1, b=-2, c=5Explanation:Step 1: Step 2: Step 3: Step 4:

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Q: 2) For x 0 solve the Euler equations a) 2" b) x²y" xy + y = x 5/² e³. --

A: The differential equation is :The aim is to solve the differential equation

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS PLS

A: 9. d.y=−x3+x510. d. x-&gt; -∞, y-&gt; -∞ and as x-&gt;∞, y -&gt; -∞Explanation:9. In the given, A…