and g are continuous on [a,b] and f(x) > g(x) for all x €[a,b] then f(x)dx> ] g(x)dx a

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Q: et [a, b] be a real interva b]→X is continuous, the is continuously differentia

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Q: (0,1). Prove the following functions is uniformly continuous on sin x f(x) =

A: Uniformly Continuous:-  Here we prove the result using a theorem of uniformly continuous.

Q: We used the e-d characterization of continuity to show in class S (x) = x² is continuous at r = 3.…

A: Given: To explain the given statement as follows, is continuos at x=3.

Q: Find the global maximum and minimum of the continuous function f(x) = x²-8 ln x on [1,4]. %3D

A: Given:F(x)=x2-8lnx        1,4

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Q: Theorem 7. Let X be a continuous RV, g a function from R to R. Let Y = g(X). Then E[Y] = E[g(X)] = /…

A: The expected value of random variable is the weighted average of all possible values of the…

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Q: For a continuous function f(x) on the set 2 [- 5,2], the net area Tx)dx must be -5 always positive…

A: The given question has been solved in detail

Q: Find a formula for LN for f on [0, 2] and compute

A: To Find: ∫02fxdx by taking the limit. Concept: For any function fx that is continuous on the…

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A: We have to apply the comparison test

Q: f and g are continuous on la,b], then F(x)+ g(x)]dx= | f(x)dx+ g(x)dx A) True B) False

A: the integral of sum of two or more functions is equal to the sum of their integrals.

Q: Let f(x) be a continuous function on R-{0} such that (f(x) dx exists for all a > 0.If g(x)= |- dt, t…

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Q: Is f(x) = ln(x) uniformly continuous on (0, 1)? Justify your response.

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Q: 25 If f is continuous and f(x) dx = 8, find xf(x²) dx.

A: given ∫025f(x)dx=8∫05xf(x2)dx=?

Q: f(x) = 1+x tan? r is f(x) uniformly continuous on [0, +o0)? Prove your result.

A: TheoremIf f:[0,∞) →R Be continuous on[0,∞) and limx→+∞ f(x)=0, f isuniformly continuous on…

Q: 3. Suppose f and g are continuous functions on [a, b] and that g(x) > 0 for all x E [a, b]. Prove…

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Q: Find the absolution extrema of f(x) = (In x)2 on [1, e].

A: We have to determine absolute extrema of girls question

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A: To prove ∫f(x)+g(x)dx=∫f(x)dx+∫g(x)dx , All are definite integrals with upper limit a and lower…

Q: 4 Suppose that f(1) 3, f(4) = 5, f '(1) = 4, f '(4) = 2, and f " is continuous. Find the value of xf…

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Q: "For a continuous function f(x), defined on an interval a , b, we have d f(x) dx = f(x), dx a…

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Q: 4. If f(0) = g(0) = 0 and f" and g" are continuous, show that %3D f(x)g"(x) dx = f (a)g'(a) –…

A: Given that f(0)=g(0)=0 and f" and g" are continuous. To show that      ∫0af(x) g"(x)…

Q: It is frequently required to solve equations of the form f(x) = 0. When f is a continuous function…

A: To solve an equation fx=0, if f is continuous on an interval a,b such that fa and fb are of opposite…

Q: 3. Let f : R→ R be continuous and let a > 0. Define g : R → R by rx+a g(x) = f(t)dt, x € R. x-a Show…

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Q: Let f and g be continuous on the closed interval [0, 5]. Suppose that J f(x)dx = A, f(x)dx = B, and…

A: Given: ∫05f(x)dx=A∫03f(x)dx=B∫53g(x)dx=C…

Q: 1. Suppose a increases on [a, b], a<xo Sb, a is continuous at xo, f(xo) 1, and S(x) 0 if x xo. Prove…

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Q: 10. If f(x) and F(x) then f(2x)dx = are continuous functions such that F'(x) = f(x) on R, %3D %3D

A: We have to solve given problem:

Q: Find a value of k making h(x) continuous on [0, 5]. kx 0 < x < 2 x + 1, 2<x < 5 h(x) =

A: The given function is hx=ekxif 0≤x&lt;2x+1if 2≤x≤5. The function is continuums. That is,…

Q: 2. If f is continuous on [0, 1] such that x* f(x) dx=0, for n=0, 1, 2, 3,.. then show that f(x)3D0…

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Q: Suppose f is a continuous function defined on (-e, e) for some e > 0 and assume that f(0) = 0 and…

A: Since function f(x) is continuous at x=0. Also given that limx→0f(x)x=C

Q: 4. If L is a Continuous function on H, then unique YEH such that L(x)=(x,y). уєн there is a

A: Given that L is continuous on H. To show: y is unique in H.

Q: Suppose that f has continuous derivative and is twice differentiable in R. Suppose that f(a) = f(b)…

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Q: b) Show that the function sin for æ e (0, 1] { f (x) = for æ = 0 is absolutely continuous on [0, 1].

A: Function is called continuous function if the left and right hand limit values at each and every…

Q: 1. Suppose f(r) is a continuous function on r E [a, b]. Prove f(x)dx < Slf(x)| dx.

A: According to our guidelines we can solve only first question and rest can be reposted.Thank you

Q: 4 Suppose that f is continuous function such that |F( x) # x and 4 [(4x)dx = 3. Then fxf(4x² )dx =?…

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Q: If f is continuous on [a,b], then the function g defined by g (x) = S f (t) dt, a < x < b is…

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Q: a In(1-x) X lim a-1 So dx

A: We can solve this using series then integral

Q: Find a value of k making h(x) continuous on [0, 5]. 0 <x < 2 x +1, 2<x < 5 eka, h(x)

A: Givenh(x)=ekx    0≤x&lt;2          x+1  2≤x≤5To find a value k when h is continuous on…

Q: Suppose that f is a continuous function on R and, g and h are differentiable functions on R.…

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Q: Can the Fundamental Theorem of Calculus be used to find x²-x+3 dx ? x²-x+3 O No, f(x) = is not…

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Q: If f(x) is a continuous function such that it is increasing on [1, 3], then Si f(x)dæ is less than…

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Q: (3x² -1, x 1, Determine c and d so that f(x) is continuous everywhere.

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Q: Prove this Let E be an open subset of R" , and let f : E → R™ be a twice continuously differentiable…

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Q: 1. Given that f is continuous on a, b|, compare f(b)(b – a) | f(x) dx, and if f is constant on a,…

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Q: b iff and g are continuous on [a,b] and f(x) z g(x) for all x E[a,b], then f(x) dxz g

A: SOLUTION-

Q: Which of the following is continuous at x=1? @ f(x)=Tx-1)² B None of the above © s(x)=/x- O f(x)=|…

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Q: Suppose f is continuous on the closed interval [a.b]. if F is an antiderivative of f for all real…

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