4 A function fx) = 1- x² + xr is defined in the closed interval [-1, 1]. The value of x in i onen intenval (-1 1) for which the mean yalue theorem is satisfied, is

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A:

Q: Let x be a ndom viable with pdf : f(x) k-x*. -1< x 1 find Yalue of k. [upto one decimal place]

A: Given that X be a random variable with pdf, f(x)=Kx4, -1&lt;X&lt;1 The value of K is obtained by…

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A:

Q: Let L2[0, 1] be all bounded Riemann integrable functions [0, 1] → R with inner product (f, g) Split…

A: Consider the provided question, Given that, Hn,kx=2n,    k2n≤x&lt;k+122n-2n,   k+122n≤x&lt;k+12n0,…

Q: Find the Riemann sum of  f(x)=x^2-4x-12 on [0,6], where the partition number is n=3 and use the…

A: Given f(x)=x2-4x-12 on [0, 6], where the partition number is n=3.

Q: if 0 < x < 1 Problem 1. Prove that f (x) is integrable using Riemann's 1 if x = 0 criterion…

A:

Q: [6] 4. Determine the Riemann sum M, using the Midpoint Rule withn=4 in order to approximate the…

A: given expression is ,  using the midpoint rule with n=4 in order to approximate the ,  ∫13(1/x2+2)dx…

Q: A sequence of non zero functions fn a nonzero function f both defined on (0, 1) such that fn 1 does…

A: See the attachment.

Q: 5. Let fn(x) ". Show that z"0 uniformly on (0, ).

A: We have to use squeeze theorem here.

Q: 20. Use Simpsons' rule to numerically integrate for the n = 6, case f(x) = x on the unit interval,…

A: Using Simpson's rule to find integration Unit interval means [0,1]

Q: Let X be the amount of soda released by a soft-drink dispensing machine into a 6-ounce cup. Assume…

A: Given information: σ=0.25 a)  P-value for the average "fill" where no more than 0.5% of the releases…

Q: An odd piecewise continuous function f(x) on every finite 00 interval of (-0, x) such that \f(x)|…

A:

Q: 10. Use Riemann sums and a limit to compute the exact area under the curve y = f(x) = 2x2 +1 on the…

A:

Q: Calculate the left Riemann sum for the given function over the given interval a.) f(x) = 3x2 over…

A: left Riemman sum

Q: Show that f„(x) = x" (1– x") converges pointwise V x € (-1,1]. Is f„(x) converges uniformly?

A: When a sequence includes a variable, it becomes a sequence of function. A sequence of function can…

Q: Adobe Scan Mar 10, 2021.pdf Page 2 of 5 Q Search Fnd for the tellenwing funtions. Sím 3x D y = y =…

A: on solving ist qestion we get

Q: arctan(2) = 1t Calculate arctan(5.5) approximately by using Trapezoidal Rule and Simpson's Rule by…

A:

Q: f fn → ƒ uniformly and the functions fn have only jump discon- sinuities, prove that f has only jump…

A: Here we use epsilon delta proof

Q: Derive a three-point formula of order O(h²) to approximate f'(ro) that uses f(xo-h), f(ro), f(xo +…

A:

Q: Let f(x) = 3x² + 2 defined on [0, 2]. Graph the function and find the average value over the given…

A: Average value of the function

Q: 3. 2- a) Find the average value of f on the interval [1, 5] b) Does the Mean Value for Integrals…

A:

Q: The question must be resolved according to the Ссо table. -B- -A- -0- -a- -y- -n- -W- 6 15 2 6. 4 1…

A:

Q: Show that the square integrable function f(x) = sin( πk log x/ log 2 )for k ≥ 1 are orthogonal over…

A:

Q: Set up a Riemann sum that would have computed the exact area under the curve f(x)3 3x+1 fromx 0…

A: We have to use Riemann Sum formula here.

Q: Let X1, , X, be iid with population pdf given by h ( which integrates to 1 over the real line. Here,…

A:

Q: Use Riemann sums and a limit to compute the exact area under the curve y = f(x) = 2x2 + 1 on the…

A:

Q: Sketch the given function and represent it as indicated. If you have a CAS, graph approximate curves…

A: We are given the function f(x)=1,   1&lt;x&lt;20,   otherwise. Now, we need to find the Fourier…

Q: 1 Test the convergence of fsin x dx.

A: To check convergence of given integral use comparison test of integrals. Comparison test: For two…

Q: sample of size n from N CO, a2) Then show That * Ex;2 is an Theorem- a X, - - be a yandom unbaised…

A:

Q: 10. Use Riemann sums and a limit to compute the exact area under the curve y = f (x) = 2x² + 1 on…

A:

Q: Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the…

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Q: 2. Use the Intermediate Value Theorem to show that 2.x 3 - if – 3 0 has a zero on the interval [-2,…

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Q: ¹).. Suppose that fn are integrable and ffn du <∞. Show that, if fn 1 f, then f is integrable and f…

A:

Q: Find the Riemann sum of f(X)=Vx on [4,9] with 4 subintervals and right endpoints. Round to the…

A:

Q: Use a linear approximation to estimate the value of sin 0.06. Verify that f(x) = satisfies the…

A: Use formula of linear approximation

Q: The volume of a section in a thread is given by=V = 4Sinx(1 + Cosx). What is the value of x that…

A:

Q: Use the methods of i. left Riemann Sum right Riemann Sum Second part Fundamental Theorem of Calculus…

A: Since there are multiple questions the first question is answered.Kindly repost if any particular…

Q: 10. Use Riemann sums and a limit to compute the exact area under the curve y = f(x) = 2x² + 1 on the…

A: Given÷

Q: Show that the midpoint Riemann sum for f(x) = x from 0 to 4 with n equal 4. subintervals is (4i-…

A: Use the formula for the midpoint Riemann sum and Substitute given function.

Q: 9. Determine if the Mean Value Theorem for Integrals applies to the function f(x)=√x on the interval…

A:

Q: 1. Express the following limits as definite integrals. (a) lim )V3(x;)² + In(x;) Ax, [2,7], where Ax…

A:

Q: Find the 3rd left Riemann sum of the function f(x)=cos x at [0,2]

A:

Q: Q3. Let f : [2, 5] HR is defined by if a is rational number 3 f(x) = -2 if r is irrational number Is…

A: I have used the definition of R integrable

Q: 9. A simple random sample of size n is taken from a population with density f(x) = x°(1+ 0), 0<x<1…

A: Method of moments:

Q: Determine the Riemann sum using L4 over the interval [-1,1]. y = 3x² - 2x + 1

A: Given function isy=3x2-2x+1_____(1)  , interval [-1,1]n=4 then,Δx=b-anΔx=1--14Δx=12

Q: (1) Use Ito's formula to compute this stochastic integral (Riemann integeral are considered done

A: Given: Let Xt is defined by stochastic integral, And its obtained by using the Reimann integral.

Q: 6. Consider the so called step function х 0 Calculate the average value of u(x) on [-1,1]. Is there…

A: Consider the given step function,

Q: Show that the midpoint Riemann sum for f(x) =x° from 0 to 4 with n equal 4 subintervals is n6 {(4i –…

A: Prove the following