The table shows selected values for a continuous functiong that is increasing over the interval [0, 4]. Using the Trapezoidal Rule, which of the following is most likely to be the value of g(x) dx? 1 3 4 2 g(x) 4 15 22 30 39 49 60 O 80 O 84 O 100 O 114 in IN

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A: Given that f(x)≥0 on [0,1] and f(x)&lt;0 otherwise. Let us recall that ∫abf(x) dx = - ∫baf(x) dx.

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

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A: given f(z)=Re(z)1+z the given function f(z) is continuous at z=0

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A: Topic- Limits

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A: Please refer tge attached image for complete solution.

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A: given

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A:

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

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A: Given, a decreasing concave up function f(x) on the interval [2, 5] with   f(2)=10, f(5)=3, f'(2)=-4…

Q: All continuous functions have antiderivatives. (A) True B) False

A:

Q: 3. Let X be the amount of an insurance claim which has following pdf: Kx (2-x), 0<x <3 f(x) = 0,…

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

Q: ALL of the following are properties of continuous functions except O a. h b is continuous at x = a O…

A:

Q: The pdf of a continuous RVX is given by f(x) = x € [1, e²]. 2x 1. Find P(X > 10). Answer: O In(10) O…

A: Note: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts…

Q: ind the constant k such that f(x) is a PDF over the given interval. f(x) = k(3x2 − x3) on [0, 2]

A:

Q: Let f be a continuous function such that | f(x) da = 13 and 10 3 f(x) dx = 8. What is the value of…

A:

Q: Consider the following function: S (x² + y²) log(x² + y²), when a² + y² # 0, 0, f(x, y) = %3D when…

A: Given function is fx,y=x2+y2logx2+y2, when x2+y2≠00,                               , when x2+y2=0…

Q: 3. Let X be the amount of an insurance claim which has following pdf: Kx2(2-x), 0<x <3 0 <x f(x) =-…

A: It is given that, x be the amount of claim with pdf fx = Kx2 2-x,0&lt;x&lt;30,elsewhere

Q: x+x², 0<x <=

A: Continuity: The function f is continuous at some point c of its domain if the limit of f(x), as x…

Q: Vhich of the following functions is continuous on the interval (- 0, + ∞ )? @ f(x) =Vx²-1 B…

A:

Q: Let X be continuous with pdf f(x) = 3x² if 0 <x< 1, and zero otherwise. Find: (a) E(X). (b) Var(X).…

A: The pdf of X is given by f(x) = 3x2 if 0 &lt; x &lt; 1 Note : According to our guidelines we are…

Q: The arc length function for a curve y = f(x), where f is an increasing function, is s(x) = V200 t +…

A: To solve this question, we have to first clearly understand that what is question actually asking…

Q: nich of the following functions is continuous at (0,0 )? ху 2x? + y? -af ( x, y ) = b. f ( x, y ) =…

A:

Q: Find a value of x, if any, at which f (x) = Vx – 64 is not continuous. ff(x)is continuous for all…

A:

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

A:

Q: Use Simpson's Rule and all the data in the following table to estimate the value of the 20 integral…

A:

Q: (c) Find a and b such that the following function is continuous at z= 1: (2² + a, z1.

A:

Q: 55. Let F be a function given by Sx2 + 1, for x s 2, 2x + 1, for x >2. F(x) = a) Verify that F is…

A: We have Fx=x2+1 ,  for x≤22x+1 , for x&gt;2 We have to verify   (a) Function is continuous at x=2…

Q: 2. Which function is bounded both above and below? B. 1. f(x) = x' S(x) = x+2 %3D С. D. f(x) = 4e…

A: Find the function which is both bounded above and bounded below: Consider: fx=x3-4x Plot the graph…

Q: O For the function $(x), fla) i defined and lem f Gx) exuts, when is fG) continuous tメO

A: Definition of continuous function: The function f(x) is continuous at x = c when: i) f(c) is…

Q: All continuous functions have antiderivatives. (A) True (B) False

A: all continuous functions have antiderivative.  But noncontinous function doesn't have. It's true

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A: Given f(x)=xv

Q: d lim g(q)d q→7 (dg

A:

Q: Find the values of c that make f continuous everywhere: x? – c2 if x 8 smaller c = larger c = Use…

A: Given function fx=x2-c2if x&lt;8cx+6if x≥8 The given function is continuous at x=8 then,…

Q: 49. The table below gives selected values for a continuous function f. If f is increasing over the…

A: Since, in the above question, there are no restrictions given. Hence, we can use the trapezoidal…

Q: Which of the following functions is continuous on the interval (-0, +)? …* f(x) = Vx² – 1 (A f(x) =…

A:

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

A:

Q: Find the constant a such that the function is continuous on the entire rea 6sin x X g(x) = a 8x if x…

A:

Q: 3. Use Simpson's rule to estimate f(x)dx from the following data -2.5 0.5 1.0 1.5 2.0 2.5 f(x)…

A:

Q: ) On what interval(s) is f increasing ? y= f{(x)} ) At what value(s) of x, if any, does f have a…

A: graph  Given graph of f'(x) determine properties of f(x) f'=0 ⇒critical points of f  f'&gt;0 ⇒f…

Q: Let f be a continuous function such that 10 1 of f(x) dx? 4 What is the value of 4 8 f(x) dx 10 1²°…

A:

Q: The graph of a function f(t) is given below. Which of the following estimates of integral 0 to 4…

A: From the given Figure it is observed that, the total area of the big square is, 4.0×100 = 400.

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: The pdf of a continuous RVX is given by f(x) = 5x*, where 0 <x< 1. o? = 05/252 02/150 025/36 049/111…

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

A:

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.