Soru 3 Suppose that f:[1,00] -R is uniformly continuous. Prove that there is a positive M such that If(x)l/x

Q: Supposef is continuous on [11, 14] and differentiable on (11, 14). If ƒ(11) = 5 and f'(x) ≤ 10 for…

A: Let's find largest possible value of f(14)=35.

Q: [1+2p(x-1)+(x-1)² x≤1 x>1 [qx+p -) -) Find the values of q, in terms of p, for which fis continuous…

A: Given:f be a function defined by:a. To find the value of q in terms of p, for which f is…

Q: 1. a. Suppose F is of bounded variation on [a,b], then |F'| = VF' a.e b. F is absolute continuous…

A: It is given that Suppose F is of bounded variation on [a,b]

Q: Suppose that a 0. Prove f() is bounded. that the function } : [a, b] → R defined by () (x) = =

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Q: [0,1] 6. If f is continuous on • prove that

A: We can solve an integral of some function f(x) w.r.t. x by using substituting, say, t=f(x) which…

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: Let fnf, where if 0<a <! { fn(x) 교프2 (2-2) if <z<i if <x<1 n п-2 2 x if 0<x<1 and f(x) | %3D if x =…

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Q: Suppose that f is continuous on that 9< f(4) < 21. [0, 4], f(0) = 1, and 2 < f'(x) < 5 for all a in…

A: Here in this question we have a function which is both continuous and differentiable in the given…

Q: 5) Suppose that f is continuous on (-00, 00). How many non-differentiable points could f have? Is it…

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Q: For the data x 0 0.3 0.6 0.9 1.2 f (x) 1 1.8221 3.3201 6.0496 11.0232 where the function f is…

A: Lagrange's polynomial is defined as: p(x)=∑i=0nLi(x)f(xi). Here, Li(x) are the cardinal functions.…

Q: 4. Prove fx=x2+4 is not uniformly continuous on R

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Q: Suppose that f is continuous at (4, 6) and that f(4, y) = y' for y + 6. What is the value f(4, 6)?…

A: Given that f is continuous at 4,6 and that f4,y=y3 for y≠6. We have to find the value f4,6. Since,…

Q: Suppose that fand gare continuous functions such that f(z)dz = 2and s(z)dz = 3, find (2f(2) +…

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Q: Let f1, f2, .. fn be n real-valued, differentiable functions.- Prove that e :[fif2 ... fn] = (fif2…

A: We have to prove that the given formula.

Q: Use moment generating functions to show that if X3 = X1 + X2, with X1 X3 - X V3 > vı, and X1 and X2…

A: Solution

Q: Suppose 10 < f'(x) < 20 for all x E R (and so f(x) is continuous and differentiable on R). Use the…

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Q: . There is a function f that's continuous at 0 and f(x) = f(2x) for all x's please show that f must…

A: Answer for sub question 1a: First step is to show fx=f2-nx for each integer n≥0. If n=0: fx=f2-0x…

Q: Assume f is differentiable. Then from the Mean Value Theorem (MVT) it follows that if f(5)0 for some…

A: Plz like ? statement of mean value theorem According to MVT, if a function f is continuous on the…

Q: If a function f(x) is continuous on (a, b) and differentiable on (a, b), then the Mean Value Theorem…

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Q: 8. A space has "the fixed point property" if every continuous function f: X → Y leaves at least one…

A: Given: 8. Suppose X is any set and f:X→X is a continuous function. The point x∈X is said to be fixed…

Q: Let f be a differentiable real function defined in (a, b). Prove that f is convex if and only if f'…

A: A function f is convex in a domain a,b if for all 0≤λ≤1, fλx1+(1-λ)x2≤λfx1+1-λfx2  ∀x1,x2∈a,b. Also…

Q: If n is a positive even integer and f(x) = Vx, then f is continuous everywhere. True False

A: Given that n is a positive integer and f(x)=(x)^1/n.

Q: Define h as x 2 Determine whether the function h is continuous h(x) = {3, x2 or discontinuous at x…

A: NOTE: Refresh your page if you can't see any equations. . if the function h(x) is continuous at x=2…

Q: For a derived varaible f : states → R is strictly decreasing if and only if for states q, q': → f(d)…

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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.