3. Using the Mean Value Theorem, show that there is a c E (0,1), such that f'(c) = 2. fx) =4x

Q: Find the normal line to f(x) = ax² - 4ax at x = 3. Assume that a is a positive constant. Next…

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Q: et [a, b] be a real interva b]→X is continuous, the is continuously differentia

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Q: Find the average value of the function LX TEX f (x) =4sin| on the interval [3,6]. COS 4

A: Dear learner, as per our guidelines we can provide the solution for first one only. Kindly post…

Q: Find the average value of the function over the given interval.

A: A function is a relation which maps each value in its domain to exactly one value in its range. The…

Q: Find the average value of f (x) = 1/x3 from x = 1/3 to x = 1/2.

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Q: Compute the average rate of change of f(x) = x2 − 2x on the interval [1, 3]. Find c ∈ (1, 3) which…

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Q: 22. Given that the average value of a function f(x) over the interval [1,4] is 5, find jos() r.

A: Given : average value of a function f(x)

Q: calculate the average over the given interval. f (x) 1] = cos x,0, π6

A:

Q: 3 b. Estimate |x*dx using Simpson's rule with n= 6

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Q: 2x,0 < x <1 Let f(x) = 10, otherwise (note that X is continuous). a. Calculate E(X): b. Calculate…

A: The question is about to find expected value, variance using given p.d.f Given : f(x)= { 2x…

Q: 20 of 21 What is the average rate of change of y with respect to x over the interval -5, –2] for the…

A: The given function is y=3x+2 over an interval -5,-2. We have to find the average rate of change of y…

Q: Find the average value have of the function h on the given interval. h(x) = 8 cos4(x) sin(x),    [0,…

A: The given function h and the interval is,

Q: Find the average value of the function over the given interval and all values of x in the interval…

A: fx=cosx,    0, π2 The average value is, 1π2-0∫0π2cosx dx=1π2sinx0π2=2πsinπ2-sin0=2π

Q: Find the average value of the function on the given interval.

A: We have to find the average value of the function at the given interval: fx=x+6;  3, 10 We know the…

Q: Take any continuous, non-negative function such that lim,oo (a) = +o0, Con- !! struct a setting in…

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Q: 3. Find the average value of f(x)=x +1 on |0,1| and where f actually takes on this value at some…

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Q: -Find the exact average value of f(x)=/2+xon the interval [2,7]. 1- 1 H

A: We have to find the value of avrage value of function

Q: Find the average value of the function over the given interval.

A: We have given function fx=secπx6 and interval 0,2. Then, average value of the function is given by…

Q: Given that f(z) =-8z +2, what is the average value of f(r) over the interval -2, 3|? (Enter your…

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Q: f (x) = (4 – æ) e² on [1,4]

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Q: Find the average value of the function f(x) = 4(x + 1)/x2 , over the interval     [2, 4].

A:

Q: 2. Find the average value of the function y = x sin(2x) on the interval [0,7 / 2]. ll the steps in…

A: To determine the average value of the function y=x sin2x on the interval 0, π2.

Q: Find the average value of the function on the giveninterval.   f(x)   = 4x -x2  , [0,4]

A: Given: fx=4x-x2, 0,4 we know that average of a function fx over given interval a,b is given by…

Q: Find the normal line to f(x) = ax - 3ax at x=2. Assume that a is a positive constant.

A: The given function fx=ax2-3ax at x=2.   Formula used:   Formula for finding normal to the function…

Q: Find the average value of the function on the given interval. ƒ(x) = x ln x; [1, e]

A: Given:             fx=x ln x ; 1, e The average value is           1b-a∫abfx dx       =1e-1∫1ex ln x…

Q: (a) Find the marginal PDFS fx(x) and fr(y). (b) What are E X and Var X? (c) What are EY and Var|Y?

A: Provided information is, The random variable X and Y have joint PDF as: fx,yx,y=x+y3      0≤x≤1=0…

Q: 4. a) Find the average value of the function over the given interval. f(x) [4, 25] Vx'

A:

Q: The pdf of a continuous RV X is given by f(x) = 3x², where () < x < 1. The median Q2 of X equals

A: Given :-   fx = 3x2                      0&lt;x&lt;1we have to calculate the median   now ,…

Q: (Which one is determined by these conditions for the bivariate functionz = f(x, y)?)

A:

Q: Q1\ A) Find average value over the given interval [1, 3] : F(x) = Vx + 4

A:

Q: find the average value of the function over the given interval. f(x)=\frac{2 \ln x}{x}, \quad[1, e]

A: The average value of any function f(x) in the interval a,b is given as =1b-a∫abf(x)dx

Q: Find the point(s) at which the given function equals its average value on the given interval. =Vx +…

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Q: Find the average value of the function on the given interval. ) = ¹ on [1, 5] X f(x) =

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Q: Compute the average value of the function f(x) = (8x^2+8x+20)e^ x on the interval [−8, 8]

A: Given

Q: What is the average value of f(x), between x = 0 and x = 5 for f(x) = 2 + sin(x)?

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture and a…

Q: 6. Given the pdf f(x)=B(1+x)-(1+B) x>0 Find the MLE of ß

A: Let x1,x2,...,xn be random sample from the given pdf. The pdf of xi is given as fxi=β…

Q: Find the average value of the function f over the interval [0, 15]. 4 f(x) = x + 1

A:

Q: Consider the function f (x) = 3 cos (x) – 5. - What is the average value of the function on [-T, 1]?…

A: Answer is given below

Q: 1. Find the average value of the function f(x) = x³ + 3x + 5 on [0,2].

A: The given function is

Q: Q1\ A) Find average value over the given interval [1, 3] : F(x) = Vx + 4 %3D

A:

Q: Find the average value of the function over the given interval f(x)= cosx ; [0, π/2]

A:

Q: p(x) = 0xº-1, x € [0, 1] show that MLE estimate for" is unbiased and give UMVUE for

A: The probability density function of X is given below: px=θxθ-1,x∈0,1 The likelihood function of θ is…

Q: In x on the interval [1, e]. 4x Find the average value fave of the function f(x) =

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Q: 1) a) Find the average value of the function over the given interval. y = 3x5 [0, 2] b) Find a point…

A: “Since you have asked multiple question, we will solve the first question for you. To get remaining…

Q: 4. Find the average value function of a) f(x) = 2x – 2x? on the interval [0,1]

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Q: sin(x/x) S(x) = [1, 2] x2

A:

Q: Find the slope of the normal line to the graph of g(x) = = at the point where x = 0. sin¯¹(x)+e²

A: Slope of the Normal line to the curve f(x) is -1f'(x).

Q: Find the average value of the function f(x) = 1 /(1 + x2) , over the interval     −3 ≤ x ≤ 3

A: The given function is fx=11+x2.

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.