1 Let f(x) x² (a) Let = (1, 0). For all p = [1, ∞], evaluate ||f||LP (M). (b) Let = (0, 1). At what value/s of p € [1, ∞] does f belong to LP (O)? O =

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Q: Is the function given by f(x)= X+5 continuous over the interval (-∞,0)? Why or why not? O Yes, f(x)…

A: the functionhere need to check the continuity over the given interval is contituous if

Q: 4) (1, 4) 2) (3.-4) (-4, 5) Determine if f is continuous at x = c. (a) x = 4 (b) x = 1 (c) x = -1…

A: Given   The graph of the function  Definition of Continuity :-  A function f is continues at x= c…

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A: We  know By definition of derivative  in interval a,b⇒f'x=limx→afx-fax-a

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A: The given function .The aim is to find the derivative of the function.Note: Since you have posted…

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A: Answer

Q: Suppose f: R → R is a function defined by f(x) = x³. (a) Find f([-1,1]) and f-¹([0, 8]). (b) Show…

A: We shall use the intermediate value theorem to answer this question

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A: we have to find out the values of x where function is continuous.

Q: 3. Let f(x) = { ,x<2 ax + b, x22 Find a and b so that f (2) exists.

A: To find the value of a and b

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A: I am attaching image so that you understand each and every step.

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A: We have to show that 1-x-2=∑n=1∞nxn-1

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Q: Let f be a real-valued function on R. Suppose that f(−1) = 3 and f'(x) ≤ 2 for all values of x. How…

A: f(-1)=3f'(x)≤2Integrating w.r.t x;∫ f'(x) dx ≤ ∫2 dxf(x)≤2x+Cf(-1)=33=2(-1)+CC=3+2C=5