2 If f is continuous on [0, 2] and f(x) dx = 5, find the value of | f(æ – 2) dæ.

Q: If f is continuous on la,b] then | tf(x)dx = f(x)dx 'a A) True B) False

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Q: 4. Find the linear approximation to f(x) = cos(x) near a =- [Where L(x) = f(a) + f'(a)(x – a) ]

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Q: Given a continuous function f(x) 2 0 at [0, 1] and f(x) < 0 elsewhere, which of the following is not…

A: Given

Q: If f is continuous and f(x)dx=10 on the interval [0,4] find xf(x^2) dx on the interval [0,2]

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Q: e that f(x) is continuous, and f'(x) is given in the figure below. y y = f'(x) 1 3

A: In this question we will use basic of calculus i.e concept of maximum and minimum. Solution of the…

Q: If f is continuous on [a,b], and f(x) > 0 then b [²√f(x) dx = a √5°₁ S f(x) dx

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Q: #46

A: We need to find the value of b such that the function g(x) is continuous at every x,

Q: Consider the function of that is continuous on the interval [-5, 5] and for which ſo f(x) dx = 4.…

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Q: If f and g are continuous on [a, b], then Lf(x)g(x)] dx f(x) dx (), 9. g(x) dx %3D a

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Q: If f is continuous and f(x) dx = 8, find xf(x?) dx. %3D

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Q: Let L{f(t)} F(s) and is a real constant. Then, 27- L{F(s-a)} =? On taf(t) OD f(at) Oo t"f(t) OD e…

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Q: Let xª sin , x + 0; f(x) ={ 0, x = 0, where a > 0 is a parameter. 1. For which values of a is f(x)…

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Q: 45. For what value of a is Jx? - 1, x< 3 | 2ax, f(x) x2 3 continuous at every x?

A: Given: fx=x2-1,x&lt;32ax,x≥3 We know that given function will be continuous at every value of x, if…

Q: For what value of b is X - b b + l' x 0 continuous at every x?

A: The given function is gx=x-bb+1if x&lt;0x2+b if x&gt;0. If the above function is continuous at x=0,…

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: Let f be a continuous function such that 5 √ (f(x) — 2) dx? What is the value of f(x) dx = -2 and…

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Q: Let f(x) = Vx and L(x) be the tangent line approximation of f(x) at x =9. Which of the following…

A: Given that       f(x) = √x  L(x) be the tangent line approximation of f(x) at x=9 . Here we have to…

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

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

Q: 2. If f is a continuous function such that S(t)dt = cos(2x)e* - [e s(t)dt for all x, find an…

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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: If f(x) continuous for x 2 0, and F(s) is defined by F(s) = | f(x) e *dx, where s > 0 Find F(s) for…

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Q: If f(x) is a continuous function on [a, b), then S(x)dx = 0. %3D Select one: O True O False

A: Given statement. If f(x) is a continuous function on [a, b] then ∫bbf(x)dx=0

Q: If f(x) is continuous on [a, b] then 4f(x)dx = 4 f(x)dx True False

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Q: of For the function f(x.y) = In (x + 6y), find- of and dy

A: It is partial derivative so when we differentiate with respect to one variable consider other…

Q: 7. If f is a continuous function such that f(t)dt = x sin x + f(t) dt for all x , find an explicit…

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Q: Suppose f(x) is continuous on R such that F(x) is an antiderivative of f(x). Furthermore i Find F(1)…

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Q: Set f(x) = xª for x ≥ 0 and f(x) = 0 for x < 0. For which values of a is f continuous at 0, and for…

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Q: has a limit at xo + 0. If Q2. Let f:R → R be a function such that f(x) x sin f is defined at xo,…

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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: If f is continuous on [a,b], and f(x) > 0 then J VFX)dx = = /J f(x)dx | F(x)dx (A) True B) False

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Q: 9. If f is continuous and f(x) dx = 14, find f(2x) dx.

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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

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Q: Given a2 +1, x 1. Is f differentiable at x = 1? Is it continuous at x = 1?.

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Q: Consider the function f that is continuous on the interval [-5, 5] and for which ſ ƒ (x)dx = 4.…

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Q: If ƒ is continuous on [a, b] and, what can you conclude about ƒ?

A: the integral given to us is ∫ab|f(x)|dx=0

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: 6. Let f be a continuous function such that f (x) dx = 9 and f(x) dx = 13. J5 What is the value of |…

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Q: (Read the dėlihition Caleluny.) |x2, if x l; is differentiable at 1. 2x-1, ifx > I; 4. Prove that…

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

A: we have to find

Q: Q: Which c.d.f. F is of X is continuous at x=0?

A: If F(0) = F(0-) then F(x) is said to be continuous at x = 0

Q: If f is continuous and f(x)dx = 4, find So xf (x?)dx. %3D

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Q: Find the linearization L(x) of the function at a. п f(x) = sin(x), a = 6 L(x) =

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Q: f and g are continuous on [a,b], then [* Grix)g(x)]dx = [(* F(x) dx)(√° xXx) dx) g(x) A True B)…

A: Given- If f and g are continuous on [a, b] then  ∫abf(x)g(x)dx=∫abf(x)dx∫abg(x)dx To determine…

Q: . For what value(s) of c is f(x) = 54-x³, x < 3) %3D lcx² + 13, x 2 3) continuous everywhere?

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Q: If x is a r.v. with c.d.f. F(x), F(x) is continuous at x = 10, then P(X= 10) = 0. True False

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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: If f is continuous on [a,b], and f(x) > 0 then (A) True B) False √√° √F(x) dx = ₁ √ [F(₂ a - f(x) dx

A: