"If a function is continuous at some point then it must be differentiable at that point". Do you agree with this statement? Give an example with proof.

Q: Give the domain of f(x) = Vx +9 in interval notation.

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Q: Find the extreme and possible points of inflection (if an exist) of f(x) = In x

A: If a function f(x) is given, to find its inflexion or extrema, first find the critical points of the…

Q: example to prove 2. Show that a constant function is continuous. Present an the proof.

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Q: 3. There are two conditions that must be met in order for a function to be continuous, explain those…

A: See a function is continuous at a point a when these two conditions are satisfied,i) ii) Note that…

Q: 4. The graph of f is given below. a) State the x-values at which the function is not continuous. For…

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Q: Let f be a measurable function ,then f is measurable.

A: I will use the property of a measurable function.

Q: Explain using theorems 4, 5, 7 and/or 9 from section 2.5, why the function f(x) = sin x + Inx is…

A: Given, fx=sin x+ln x. To show that the function is continuous at every number in its domain.

Q: 7. Let A = (1, 2, 3, 4, 5) and define a function F: 9(A) Z as follows: For all sets X in P(A), 0 if…

A: Function value whose domain is a power set

Q: decide if the given statement is true or false,and give a brief justification for your answer.If…

A: The given statement is false. Explanation: A function f is periodic if there exists a positive…

Q: 3. Let (0 < x < 1) x; f(x) = { (1 < x < 2) 2x; i) Is the function f(x) continuous on [0, 2]? Explain…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: f(x) = 523 -5x + b if r ≤ 9 if x > 9

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Q: Suppose that f(x) is a continuous function with f(1) = - 6 and f(5) = 6. Determine which choice best…

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Q: Find the values of a and b that make f continuous everywhere. x²_ X-2 ax² - 6x + 3 2x = a + b a ||…

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Q: Create a piece-wise function that is NOT continuous and has domain (−∞, ∞)

A: Let f(x) be a piece wise function, that is not continuous and extends throughout the domain of real…

Q: Is it true that a continuous function that is never zero on an interval never changes sign on that…

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Q: Given the function fx) whose graph is shown below, determine 4-3). Do not include "f(-3)=" in your…

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Q: Does the domain of the function f(x) = VI +x include x = -27

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