3. (i). Every uniformly continuous function is a Lipchitz function. (Prove or Disprove)

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A: Given problem:- True or False, and give a short reason:   (a) If a function is differentiable, then…

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Q: (a) Given a continuous function f RR and a connected subset SER, is f-¹(S) connected? Justify your…

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Q: (c) If f(x) is continuous on a closed interval [a, b] and f(x)dx > 0, then f(x) > 0 for some x E [a,…

A: Since you have asked multiple questions in single request.so we will answering only first question.…

Q: Problem (3) Show that if a continuous function f is holomorphic outside a line in C then it is…

A:

Q: Find the intervals on which the function is continuous. f (x) = 4x x²+4 -6 -4 -2 Af -2 -4 O (-∞, 1),…

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Q: Let f(x) be a continuous function. If f(c) is an absolute max or absolute min, then c is unique. O…

A: Given,  fx is a continuous function fc is absolute max or absolute min , then c is unique.  We have…

Q: Which of the following functions are continuous on the interval 1 < x < 7? A. h(x) B. f(x) = 2² +²36…

A: In this question, we will check the given function is continuous.

Q: Q4) let f be non-negative continuous function of [a, o]& k> 0 is constant. IF t f(t) a holds, then…

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Q: Mathematicians I. Perepelitsa and C. Douglas are having an argument. Professor Douglas claims that…

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Q: webassign.net/web/Student/Assighment-Responses/ Fautosave#Q12 Аpps YI we Tlave LiidL 12. [2/3…

A: The differential equation is - y''-2y'-3y=6x+4

Q: If f is a continuous function on (-4, 4) whose graph is in 1. ƒ"(x) > 0 on (-4,-2) 2. (0, 1) is an…

A:

Q: 3 (-1,2.625) -2 -1 4 N 0 -2- (-2,-2.25) -4 Graph of f(x) 1 2 Given the graph of the continuous…

A: Solution : From the given figure it is clear that

Q: h(k) = V5 – k + Vk + 9

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Q: n a and b with f(c) = N. I thi

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Q: 4. If continuous function f:[0,1] U (2,3) → R is one-to-one, is f also continuous? 1

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Q: 7. For each of the following, give an example of functions f: A → B and g: B C that satisfy the…

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Q: Mark the correct answer. Let f be a strictly increasing and continuous function defined on the set…

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Q: Find the values of constants a and b that make f continuous on (-o0, +o0) where 2x +1 if a 5 f(x) =…

A: Use definition of continuous function and find the value of a and b

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.