2. By using Simpson's rule with N = 4 , 8 , and 16 Integrate the following functions

Q: 1. Evaluate the following integral: la 2x³ 2x5-x-4x³ + 1 (a) analytically, (b) single application of…

A: NOTE: As per the guidelines we are supposed to answer only 3 subparts question. Please upload it…

Q: Two equivalent forms of the Chain Rule for calculating the de-rivative of y = f(g(x)) are presented…

A: Given, if y=fx and u=gx then the derivative of their composition can be expressed as

Q: Suppose that T(0) = a and T(1) = b are some constants. Define the running pairwise average as, for n…

A: Given: Tn+2=12Tn+1+Tn for n≥0 T0=a T1=b To find: The limit of Tn as n→∞.

Q: Find the maxamin s in flectlon Points and the in ter Vals on which the function inerease,decrease…

A: follow the solution which is mentioned in step 2.

Q: (1) Use the trapezoidal rule and (2) Simpson's rule, with n= 10, to approxima te the integral. Round…

A: Topic : numerical methods

Q: how do you find z sub alpha over 2 using table a-2

A: I am solving this question by taking an example Let us take α = 0.05 We need to find

Q: 7. Evaluate the Integral S (x + 3) dx

A:

Q: Evaluate L 8y (x³ + 1)² 2y by reversing the order of integration. dady

A:

Q: 1 (b) Evaluate the integral S ; dx 2x2-12x+26

A: To evaluate: The integral of . Formula used: Integration Formula:

Q: Find the integration inner product on C[-4, 2] of the given functions. f(x) = 20x g(x) = 3x3 %3|…

A:

Q: 1,3 2,1 3,4 f(x) 2,6 3,5 3,2

A: The given tabular data is,

Q: 4 Find the linearization of the function f (x) = x² at x = 1. L(x) = Using this linearlization, ƒ…

A: f(x)=x4 at x=1 So, L(x)=f'(1)(x-1)+f(1)

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

A:

Q: 2. a) Evalute the following improper integrals dr 3

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the remaining…

Q: 12. Find the dicections at.which. the directronal.derivative af.f.(hg)..xSin xy.at.(,a).has.…

A:

Q: Let p(x)= e5x be the standard integrating 3 factor to x y' +p(x)y =x°. Find p(8).

A: We have to find the value of p(8).

Q: (3) A study on optimizing revenue from a website considered dividing cus- tomers into two groups…

A:

Q: Find an integrating factor to the linear D. E. In(9 x+16)y+ y =20 9x +16 p(x)= (6 x+ 14) In(18 x…

A: Given the linear D.Eln (9x+16)y'+99x+16y=20we need ti find the integrating factor

Q: 3. Compute x' In x dx both analytically and numerically. Use trapezoidal, Simpson's 1/3, Simpson's…

A:

Q: Find an upper bound for the Lagrange interpolation error for f(x) sinh(x)+2 cosh(x) over the…

A: Given: fx=sinhx+2coshx, x∈0,2. Interpolation nodes xk=k4, k=0,1,⋯,8. To find:          An upper…

Q: A function f(x) contains the following points: (1.00, 0.90), (2.00, 3.00), (3.00, -4.50), (4.00,…

A: Given information: A function f(x) contains the following points: (1.00, 0.90), (2.00, 3.00), (3.00,…

Q: Compute an approximation to the value of Le-x*dx a) using Simpson's Rule b) using Simpson's…

A: The composite Simpson's rule approach is a frequent way to deal with issue. To accomplish this,…

Q: 3. Show that for p> 1 and r E (0, 1), the integral below converge: dt tp

A: by limit convergence test we cab prove this, we have to treat the definite integral as summation…

Q: How large should n be to guarantee that the Simpson's Rule approximation to 11 (e^x^2) (bounds 1…

A:

Q: Suppose that T(0) = a and T(1) = b are some constants. Define the running pairwise average as, for n…

A: Given: Tn+2=12Tn+1+Tn for n≥0 T0=a T1=b To find: The limit of Tn as n→∞.

Q: Find the root of f(x) = (x – 4)° (x +2)= 0, using the initial guesses of X2 = -2.5 and Xy = -1.0,…

A: Note:- For this problem any particular method is not mentioned. so, here i'm using Bisection Method.…

Q: use Simpsun mle to tind dhe fulluwing integration , use n=3 How o-6, X ė d x O. 3

A:

Q: Find the integration inner product on C[–4, 1] of the given functions. f(x) = 15x g(z) = 3r* (f, 9)…

A:

Q: 5) Construct a linear approximation of the function f(x ) = lacX+s) about the point x,= 1. Compare…

A: Tangent line approximation or linear approximation is very significant in differential calculus.…

Q: 4. Find two values of c in [-4, 4] such that f(c) is equal to the average value of f (x) = 3 cos 2x…

A: To determine c such that f© is equal to the average value of f(x).

Q: Find the integration of (1+ 2x)dx using Trapezoidal and Simpson's Rules for n=6

A: Given integral  ∫061+2xdx The Trapezoidal rule states that…

Q: Determine the approximate integration of the following using simple & modified trapezoidal,1/3…

A: Only one question or maximum 3 parts are allowed . I did 1st integral , for other 1 please repost

Q: 7 If the change of variables u = x-1 is used to evaluate the definite integral f(x) dx, what are the…

A: This question can be solved using the concept of change of limits in definite integrals.

Q: In the gas pipeline of Cactus, Tab. to Reynosa, Tamps. The cost W(Ton/hr) is determined periodically…

A:

Q: 2. Consider the function f(x)=sin(x) on the interval [0,1]. Use theorem(3.3) to determine the step…

A: Given function is f(x)=sinx Interval is [0,1] Solution a: For linear interpolation N=1 So…

Q: Let X1,..., Xn i.i.d. N(H, o2), where both parameters are unknown. (a) Show that the UMVU estimator…

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: Find the Integration of: Ja (3sint + esin t) cost dt In 3 2

A:

Q: Find the integration inner product on C[–4, 2] of the given functions. f(x) = 15x g(x) = 2x³ %3D…

A:

Q: How large should n be to guarantee that the Simpson's Rule approximation to 5(e^x^2) (bounds 1 and…

A: F is continuous on 4th derivative over the interval [a,b]. the error of integral f(x) is given by

Q: II z= ě Y x - Juv Find dz dv üs ing chein rule.

A:

Q: Find the net change in ve]locity over [1, 4] of an object with a(t) = 8t − t2 m/s2.

A:

Q: 3. Estimate the integral v2 + x² dx using appropriate of Simpson's rule with step size, h = 0.2.

A:

Q: Determine general antiderivatives for each of the following functions (use capital C as the…

A: a. Given. f(x)=x3x4-5

Q: 39. Use Leibniz's Rule to find the value of x that maximizes the value of the integral px+3 1(5 – t)…

A:

Q: Find the integration inner product on C[-3,3] of the given functions. f(x) = 16x g(x) = 3x² (f, g)…

A: Explanation of the answer is as follows

Q: 5. What is the most general antiderivative of the function S(2) = z - 2, in other words, what is -…

A:

Q: 1. Use the Gauss forward formula with xo = 2.0,h = 0.15, n = 7 to find an estimate for f(2.5) if %3D…

A: Given: fx=xlnx. x0=2.0, h=0.15, n=7.   We can solve this by using Gauss forward formula