Suppose that f and g are continuous functions such that 3 | f (2) f (x) dæ = 2 and | [2f (2) + g (x) dx 3, find (x)] dx.l

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: If f is continuous and f(x) dx = -1, find f(2x) dx.

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Q: Is there a sequence of continuously differentiable functions: fn : R –→ R such that fn → x and f. →0…

A: Yes, the sequence is given in step 2.

Q: 10 If f is a continuous function and F'(x)=f(x) for all x € R, then x)dx=?

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Q: Find the values of α and β such that the function f(x) =αcosx + 2 if x < 0  and f(x) = βe3x + αx2…

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Q: 36 If f is continuous and f(x) dx = 6, find xf(x²) dx.

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Q: 6. If f is continuous and f(x)dx=4 , '3 | xf(x?)dx=

A: Explained below

Q: Find a and b such that f(x) is continuous at x=1. [x – 2] + a x 1

A: A detailed solution is given below.

Q: If f(x) is a continuous function on [3,7] and F(x) is an anti-derivative of f(x) such that F(3)=7…

A: Given :f(x) is continuous function 3,7Fx is anti-derivative of fxF3=7 and F7=3To determine…

Q: Suppose that a continuous function g satisfies: g(x)dx = 42 and g(2x)dx = 3. %3D 2 Find æg(3x²)dx.

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Q: Suppose that f is a function on the interval [1, 3] such that –1 < f(x) < 1 for all x and f(x) dx…

A: It is given that ∫13fxdx=0 and -1≤fx≤1.

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: Suppose f is a continuous function such that Si f(t)dt = e® In(x) for all x > 0. What is the value…

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Q: Let f be a continuous function such that | f(x) dx = -10 and | f(x) dx = 9. What is the value of…

A: Given: Let f be a continuous function such that ∫52fxdx=-10 and∫-25fxdx=9. To Find: What is the…

Q: Suppose that f(a) = f(b) = g(a) = g(b) = 0 and the second derivatives of f and g are continuous on…

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Q: If f is continuous and f(x)dx=4, | xf(x?)dx=

A: We will find the value of the integral as following.

Q: 81 xf(x²) dx. 6. If f is continuous and f(x) dx = 4, find

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Q: Suppose that f(1) = 4, f(4) = 5, f '(1) = 6, f '(4) = 3, and f " is continuous. Find the value of xf…

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Q: Suppose that f (x) is a continuous function, f(-1) = 6, f(2) = and f(x)dx: = -3 = T. Evaluate the…

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Q: Suppose that f (x) has a continuous second derivative f"(x), f(2) = 4, f'(2) = –1, and / f(x) dx =…

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Q: Suppose that f(1) = 2, f(4) = 8, f'(1) = 10, f'(4) = -3, and f" is continuous. Find the 4 value of…

A: We have to find the value of the given integral.

Q: 4). If f(1) = 12 and f' is continuous and | f'(x) dx=17, what is the value of f(4)?

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Q: Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x ≥ 0…

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Q: - if f(x) is a continuous function at x O, then a = 1-cos4x よく0 x? { a If f(x) = r= 0 r>0 V16+ VF -

A: Then to find the value of a if f(x) is continuous at x=0   Since for any continuous function at…

Q: 9. Suppose f(x) is continuous and f(x)dx = 10, f(x)dx the equation f(x) = 1 has a solution on the…

A: Divide the interval [-5,5] in to two sub intervals [-5,-1] and [-1,5]

Q: Suppose that f(1)=8, f(4)=−4, f′(1)=−3, f′(4)=2, and f′′ is continuous. Find the value of ∫from 1 to…

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Q: If f is continuous and f(x)dx=4, xf(x2)dx=

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Q: Find the best linear approximation to f on th e interval [0, 1].                            f (x)…

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Q: Iff is continuous on [a,b], and f(x) 20 then A True False ر VFX √f(x) dx = dx = √5 F(x f(x) dx

A:

Q: Suppose that f (x) has a continuous derivative, сп/2 f(-1/2) = 0, f(T/2) = 1/4 and f (x) dx = 3.…

A: The method of substitution is a very significant method in evaluating definite integral. The…

Q: b) Show that the function f (x) = { * x² sin ! for x E (0, 1] for x = 0 is absolutely continuous on…

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Q: 6- if f(x) is a continuous function at x = 0, then a = 1- cos 4x x0 V16+ Vx -4 3.

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Q: Let f be a continuous function such that f (x) dx 5 and 6° | f(x) dx = 3. What is the value of |…

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Q: 10 If f is a continuous function and F(x)=f(x) for all x€R, then | f(Gx)dx=?

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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: Let g be a continuous function. Using the substitution u = 3x – 1, the integral (g (3x – 1)) dx is…

A: We can use the concept of method of substitution in order to solve the given problem.

Q: If f is continuous on [0, 1], prove that f₁¹ f(x) dx = f₁¹ ƒ(1 − x)dx.

A: This question can be solved using properties of definite integrals.

Q: Suppose that g(x) is a continuous function, g(0) = 2, g(1/2) = 1 and g(x)dx = 3. Evaluate the…

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Q: f is continuous and f(x) dx = 8, find xfc

A: we have to find

Q: If f and g are continuous on a <x< b, then S) + g(x)] dx = Sf(x)dx - g(x)dx %3D

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

Q: '18 6. If f is continuous and f(x) dx = 16, find f(2x) dx. %3D

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Q: What is the continuous extension of f(x) = at point x-1. x -1 x2-1' %3D x +x-2 find dy dx

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Q: Suppose that a continuous function g satisfies: g(x)dx = 42 and | g(2x)dx = 12. 2 | #g(3x²)dx. Find

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Q: Suppose that the function f is continuous everywhere. Suppose that F is any antiderivative of f, and…

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Q: Let f be a continuous function such that f (x) dx = -4 and 1 f(x) dx = –14. What is the value of 2…

A: As we know that;  The properties of the definite integral; 1). ∫abfxdx=-∫bafxdx…

Q: 4 '2 If f is continuous and f(x) dx = 10, find | F(2x) dx. %3D

A:

Q: If ƒ(x) is continuous [-00,b]then on ſf(x)dx= lim [ ƒ (x)dx а. a a

A: Explanation of the solution is given below...

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

A: A function is continuous if limx→a+ h(x)  = limx→a- h(x) = h(a) Now in the given question, function…

Q: (b) FIND the value of c, so that f(x) = {cx – 1, x< 0 lx² – 1. x 2 0 is continuous everywhere.

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Q: For all continuous function f: [0, +o] → R, a > 0 we need to prove that 2*f) dx = [ xfw)dx

A: