= Let f [1,1] → R be a continuous function which is odd, f(x) -f(-x). Show that then, there is a sequence of polynomials which are odd and which uniformly converge to f.

Q: Suppose f: (0, 1)→ (0, 1) is a surjective monotonic function. True or false: The function f is…

A: f: 0,1→0,1 is a surjective monotonic function.

Q: Determine if the function is continuous at the indicated point 12 1 f(z) = |2|= 1

A: To determine if the function f(z) is continuous at ∣z∣=1, we need to check the following: The value…

Q: Suppose f(x) is continuous on [3, 8] and -5 < f'(x) < 3 for all x in (3, 8). Use the Mean Value…

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Q: Find constants a and b such that the function 3– bx, if x>-2 f(x)=- -1, if x=-2 ax – bx, if x<-2 |…

A: Given query is to find the value of a and b.

Q: 21) Write a function that has an infinite discontinuity at x = 100. 22) Write a function that is…

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Q: a)Find the average of the function f(x)= x² +1 on the interval [-1,2] Answer:

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Q: What is an example of a function f : [2, 3] -->R which is not continuous at 1 but which is…

A: Here's an example of a function that is not continuous at 1 but is integrable on the interval [2,…

Q: If f is continuous on the interval [5, 12] and f(5) = 7 and f(12) = -2, then f must have at least…

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Q: VI. Let f(x)=x²-x²-x+1 on [-1,2]. Find all numbers c satisfying the conclusion to the Mean value…

A: Let fx=x3-x2-x+1 on -1, 2.To find all numbers c satisfying the conclusion to the Mean value theorem.…

Q: Q3\ a) Find the values of a and b to make the functions continuous at every x: ax + 2b 2) g(x) = }x²…

A: Given function is,  f(x)=-2        ;x≤-1ax-b   ;-1≤x≤13          ;x&gt;1

Q: Let f: R → R be a function such that f(r) 2 r, for all z € R. Show that if f(an) converge, then Σa,…

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Q: Let f be continuous on [-1,5], where f(-1) = 12 and f(5) = 6. Can we conclude that a value -1 < c <…

A: Intermediate value theorem states that if 'f' is a continuous function over a closed interval [a,b]…