Using the following normalized test function for a particle in a box of width a: 30 y(x) = V x(a - x) for 0

Q: 18. The velocity v of a particle at distance s from a point on its path is given by the table: s ft:…

A: Given,

Q: 1 et f(x) = = . X Find the tangent line to the graph of the function at x = −1. y = 【 Find the…

A: Follow next step

Q: 3. The edges of a cube are measured to be 5cm long, with a maximum possible error of 0.1cm. Using…

A: Given : Length (s) = 5 cm  Error (ds) = 0.1

Q: 3 Let f(x,y) = 16xy²0<x < 2,0 < y <2 a. Show thatf (x,y) is a valid PDF b. Find the marginal…

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

Q: 20. The average value of f(x) = from x = 1 to x = e is %3D %3D 1 (A) e +1 (В) 1-e (С) е -1 1 (D) e-1

A: Putting average value function formula we can get

Q: ;Find the average value TX of the function f (x) = 4sin Cos on 2 2 the interval [1,4].

A: According to Bartleby's policy we are allowed to solve only 1 question at a time. Here's the…

Q: 21 For the position function st)t+1. Complete the following table with the appropriate average…

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Q: 2. The velocities of a horse at selected times over a 60-second time interval are given by the table…

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Q: Determine the average value of the function y = 3 sin( [ n/ 9] x) on the interval 0 s x 9. 3 2.5 2…

A:

Q: A flexible cable suspended between two vertical supports is hanging under its own weight. The weight…

A:

Q: . A vertical line segment of length 8 ft is moving horizontally at a rate of 3 ft/sec. At what rate…

A: We have to find the rate at which area is being swept out by the moving vertical segment.…

Q: A mass m moves along the x-axis subject to an attractive force given by 19mx/2 and a retarding force…

A: Maximum amplitude of a driven, damped oscillator can be found using the relation…

Q: (b) (i) The measurement of the edge of a cube is found to be 15 inches, with a possible error 0.03…

A:

Q: 4: The design of a new airplane requires a gasoline tank of constant cross-sectional rea in each…

A: To find the area, use the Simpson's rule formula, Area=∆x3y0+4y1+2y2+4y3+2y4+4y5+y6. To find ∆x, use…

Q: The outflow concentration from a reactor is measured at several times over a 24-hour period: 10 t,…

A: Note: Here, the number of points are 10 which is even. So, Simpson's 1/3 rule is not applicable…

Q: Find the average value of the function J (1) = VI +1 from x =0 to x = 3.

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Q: One model for the spread of epidemics assumes that the number of people infected changes at a rate…

A: Here we will verified the given solution.

Q: 41. f(x) = cos x, [0.]

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Q: (7) Find the average value of the function over the given interval (a)f(x) = 4 – x², [-2, 2] (b)…

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Q: Sheet 5 Numerical analysis QI/ Evaluate f (x² + 3y?) dy dx using Simpson's 1/3 rule in x-axis and…

A: NOTE:- AS POSTED MULTIPLE INDEPENDENT QUESTIONS. WE ARE ANSWERING ONLY FIRST QUESTIONS FOR YOU AS…

Q: 1- Find the average rate of change for y = xo = 1 x, = 2 2- Find the instantaneous rare of change…

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Q: (a) Is first order stationary (b) Has total average power of 61 W

A:

Q: A flexible cable suspended between two vertical supports is hanging under its own weight. The weight…

A:

Q: The probability that a radioactive substance will decay at time t is modeled by the density function…

A: From the given information, the probability that a radioactive substance will decay at time t is…

Q: 13. The capacity of a battery is measured by |i dt, where i is the current. Estimate, using suitable…

A:

Q: 19. Find the average value of f(x, y) = sin (x + y) over a. the rectangle 0 < x < ™, 0 < y<. b. the…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Determine the RMS value of y=Vx over the range of x=0 and x=1

A:

Q: 1 Let f(x) = a) Find the tangent line to the graph of the function at a = 1. %3D y 3D b) Find the…

A: Given - f(x)=1xWe need to find tangent line and normal line to graph of function at x=1 Slope of…

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

A:

Q: Q2: Suppose the electric potential at (x, y) is given by f(x, y) = 0.5 Ln(x² + y²) estimate the…

A: In this question, we have to find the error in f(x,y) and percent relative error for the given value…

Q: 3. Consider the function e-x/127.0. a. Normalize it so that it is a PDF on [0, 0). b. Compute the…

A: As per guidline, we can answer first 3 subpart of question.

Q: Find the average value of the function f(x) = 4 sin x on the given intervals. %3D a) Average value…

A:

Q: Find the average rate of change of the function y = 2e2 with respect to x over the interval from x=0…

A: As we know that; The average rate of change between the interval a≤x≤b is given by; Avereage rate of…

Q: Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water…

A: Given: Let us consider the given, dhdt=-56h32 c=0.6, g=32 ft/s2 Vertex angle=60°

Q: 1) Find the average rate of change of the function over the given interval. a) f(x) = x + 1, [2,3]…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: A tank in the shape of a cylinder standing on end leaks water through a circular hole in its bottom.…

A:

Q: Y1 0 zero elsewhere. Find Pr(Y1 < 1/3)

A: # Given: y1&lt;y2&lt;y3&lt;y4 be the order Statistics from exponential distribution then  to find…

Q: The amount of heat dissipated by a convective heat exchanger is governed by the equation Q=(AT)(A)/C…

A: Given The amount of heat dissipated by a convective heat exchanger is governed by the equation…

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

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Q: (b) Show that Y = log () is exponentially distributed with rate parameter 0, that is, the pdf of Y…

A: Solution

Q: a. What is the joint marginal PDF of X and Z? b. What is [P 0 <= Y <= 3/2 | X = 1/3 Z = 5/2]?

A:

Q: A conducting bar of uniform cross-section lies along the x-axis, with its ends at x 0 and x = 1. The…

A: Here fx=lx-x2, 0≤x≤l.

Q: 22. Find the slope of the normal line to y = x + cos xy at (0, 1). (A) -1 (В) 1 (C) 0 (D) Undefined

A:

Q: (b) Find the joint cdf of (X,Y). (c) Find the Marginal pdf of X and of Y. (d) Are X and Y…

A:

Q: 1. Find the average value of the function f(x, y) = sin(r+y) over the rectangle 0 < a < 27 and 0 < y…

A: Given: fx,y=sinx+y and R:0≤x≤2π,0≤y≤π2. To Find: Average value of given function over given…

Q: The velocity is equal to the rate of change of distance x (m), dx v(t) dt (1.1) a. Substitute Eq.…

A: After substituting Eq. (1.2) to Eq. (1.1), we have dxdt=gmc1−e−cmt

Q: A flexible cable suspended between two vertical supports is hanging under its own weight. The weight…

A:

Q: h(x) = cos*x sin x, [0, ]

A: The function is h(x) = cos4x sinx, on the interval [0, pi]. We have to find the average value of…

Q: Find the average value of: f(x) = 9 sin x + 8 cos a on the interval [0, 8π/6] Average value=

A: The average value of fx=9sinx+8cosx on the interval 0,8π6

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.