Let f be Riemann integrable on J and let f(x) > 0 for x € J. Show that

Q: Let f(z) = { -2 <z50 0, =-2 then f is Riemann integrable True False

A: True

Q: Answer the following True or False. If f(x) is integrable on a, b, then f(r) is continuous on [a,…

A: For the solution follow the next step.

Q: Let f,g:[a, b]-X are Riemann integrable , f-g is Riemann integrable.

A: Let f,g:a,b→R are Riemann integrable.To prove that f-g is Riemann integrable.

Q: Let f (2) = #{1- ()*}. 1-()}, a – B 0. Find k so that fis a density.

A:

Q: 1) Let f be integrable on an interval [a, b] (with a < b). Let m and M be the infimum and surpemum…

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Q: Suppose that f is integrable on [a, b] and g is integrable on [b, c]. Let f(x) x [a,b) h: [a, c] → R…

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Q: Let f,g: [a,b]-R are Riemann integrable , f-g is Riemann integrable. ylgn

A: True.

Q: 10. If f(z). g(z) is integrable on [a, b). prove that (z)g(x)dx f(z)dx g(x)dr.

A: Given that, f(x),g(x) are integrable on [a,b]. The aim is to show that…

Q: f(x) is increasing and bounded on [0, 1], then f(x) is Riemann-integrable on [0, 1].

A:

Q: To prove Let I CR be an interval, and let f:I→ R be a Riemann integrable function. Then f is also…

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Q: 5. Let D = [0, 1] × [0, 2] be a rectangle in R? and define the function f : D → R by f (x, y) = 4 –…

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Q: (1) Let f be integrable on an interval [a, b] (with a < b). Let m and M be the infimum and surpemum…

A: Solved below

Q: Consider the following theorem. Theorem If f is integrable on [a, b], then = lim f(x;)Ax n- 00 la i…

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Q: 3. If f : [a,b] → R is a bounded function such that f(x) = 0 except for x in {c1, C2, .., Cn} in [a,…

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Q: 4. Let f(x) = x, Vx E [0, b]. Show that f is integrable and that 62 f(x) dx : Answer:

A: Given function is  fx=x, ∀ x∈0,b

Q: Let f is Riemann integral ,Ifl is integrable and a صواب İhi

A: The solution is given as

Q: Let f is Riemann integral ,Ifl is integrable and

A: True

Q: The tangent function f (x) = tan x is integrable from 0 to T. O True O False

A:

Q: Suppose that h is integrable and that , h(r) dr = 0 and ſ, h(r) dr = 6. What is h(r) dr ?

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Q: 4. Let f: [a, b] → R be integrable. Define F: [a, b] → R by F(x) := f* f(1) dt a Show that F is of…

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Q: Every function which has counatable discontinuous points on [a,b] is Riemann integrable on [a,b]. *…

A: See the solution below.

Q: Every function which is Riemann 0/3 integrable on [a,b] is continuous. * True O False

A:

Q: Use the Sequential Criterion for Integrability to show that if f: IR is Riemann integrable on I =…

A: The main objective is to prove that if f is Riemann integrable then cf also Riemann integrable.

Q: 4. Let f: [a, b] → R be integrable. Define F: [a, b] → R by F(x):= == f(t) dt Show that F is of…

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Q: Suppose that h is integrable and that h(r) dr = 0 and L h(r) dr = 6. Find Ги a. h(r) dr b. h(u) du

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Q: Evaluate function given assuming ƒ is integrable on [a, b].

A: We have to calculate,∫abf(x)dx+∫baf(x)dx = ?            ...................(1)As function f(x) is…

Q: Let X,y EIR. Prove that if 21 x +35 y = 45 then x and y are not both integes.

A: Given: Let x,y∈ℝ. To prove: If 21x+35y=45, then x and y are not both integers.

Q: Are the following functions Riemann Integrable to their corresponding in- tervals? Explain your…

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Q: Let f : [a, b] R be a function defined by 0if rEQ . if r¢Q f(x) = %3D Show that f is not Riemann…

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Q: Consider the function defined on the closod interval (a, b) as f1 if I=c h(r) = if Itc where a <c<b.…

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Q: Suppose that f and g are integrable and that f (x) dx : :-1 | f(x). h(x) dx = 4 Odx = 5 Use the…

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Q: Show that f(x) = x² is integrable on [a,b].

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Q: Let ƒ be a Riemann integrable function on [0, 1]. n (i). Let g be in (0, 1). Find lim La n→∞…

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Q: Let f,g:[a,b]→R_are Riemann integrable , f-g is Riemann integrable.

A: Given a statement

Q: Show that, if f and g are Reimann integrable on [a, b] then f - g is Reimann integrable on [a, b],…

A: We have to prove that following identity.

Q: Show that if f is Riemann integrable [a, b] and f(r) 0 for all r € [a, b], on f(x) dr 2 0.

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Q: True or false If f is integrable over [a, c], then for any b ∈ [a, c], R b a f(x)dx + R c b f(x)dx…

A: Consider the provided question,

Q: Consider the following theorem. Theorem If f is integrable on [a, b], then F(x) dx = lim s fx,)Ax n-…

A: Given- Consider the following theorem. Theorem  If f is integrable on a, b, then ∫abfx dx = limn→∞…

Q: Let f : [0, 1] → R be defined by f(x) : = x. Show that f ∈ R  [0, 1] and compute ∫^1_0(f) using the…

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Q: F is Riemann integrable on IFI is Riemann integra ble

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Q: = Use the Riemann's Criterion for integrability to show that the function f(x) integrable on [0, b]…

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Q: Let f be a Riemann integrable on the closed interval [a, b]. What is the Lebesgue set of f?

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Q: Let f(x) = x² sin – if x # 0 and f(0) = 0. Then ƒ Reimann Integrable True False

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Q: Consider the following theorem. Theorem If f is integrable on [a, b], then f(x) dx lim f(x;)Ax %3D…

A: This way of evaluating definite integral is known as " Integral using limit of sum " Here we will…

Q: Are the following functions Riemann Integrable to their corresponding in- tervals? Explain your…

A:

Q: Suppose that f and h are integrable and that: frx) = -1 , , f(x) dx = 5 , ,h (x) dx = 4 ,Find: a. -2…

A: We have to find the given integrals.

Q: Please just do 3(b).

A: (b) To prove that the given function is not Riemann integrable using Lebesgue;s theorem

Q: Let f be the function defined by fx)=1+x, when 0<x<}, }<x<1 0, when x . Show that fis integrable…

A: We know that  A bounded function f which has only a finite number of points of discontinuity in…

Q: Let f(x) = x² on [0, a] , a > 0. Find the Lower Riemann integral and Upper Riemann Integral, Check…

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.