Calculate the limited expansion centered on the origin, of order n for f(x) = cosh(x) + sinh(x²) f(34) (0), What is the value of

Q: (x² + 1)cos x x4 -x + 2

A:

Q: Determine if the improper integral converges or diverges: 1 dx. 1+x²

A: Our Aim is to determine whether the improper integral given below converges or diverges∫0∞11+x2 -(i)

Q: 1. Use the definition of the definite integral as the limit of a Riemann sum to evaluate - 4)² dx.

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

Q: Find the rate of convergence for lim h-0 sin h - h cos h2 0.

A: Given that limh→0sinh3-h3cosh2h=0. The rate of convergence can be calculated by evaluating the…

Q: Compute the Riemann sum L4 for the function f(x)=2 cos x on the interval [0, 7]. Enter your answer…

A: To find the left riemann sum.

Q: Conclude on the convergence or divergence of sin x dx cos x

A: Since function is not continous at x=pi/2. Hence we break the limit of integral at x=pi/2. This…

Q: Determine maximum error between 0 ≤ ? ≤ ?/3 interval for fourth degree Taylor expansion of ?(?) =…

A: Determine maximum error between 0 ≤ ? ≤ ?/3 interval for fourth degree Taylor expansion of ?(?) =…

Q: Q3) Use Riemann sum to evaluate the definite integral: 2 | (2x + 1)dx where n = 0.4

A:

Q: The area above the x-axis, below the graph of f(x) = between x=0 and x=2 is the limit of 1+z which…

A:

Q: Find out if the improper integral converges or diverges. If the given converges, find its value.…

A: Solution

Q: Approximate the area between the graph of f(x)=x^3 and the x-axis on the interval [3,5] by using a…

A:

Q: Use Simpson rule’ 1/3 Method with (n = 6) to estimate the integral f(x) = x / ((9*x^3)-3), where a=…

A: Fghhhj

Q: 10. Determine whether | sin(x)dr converges or diverges. If this improper integral converges,…

A:

Q: Determine the convergence of the integral tan x dx. (In(cos x))? COs x

A: The given integral, ∫π3π2tan xlncos x2dx

Q: 1- Estimate the minimum number of subintervals needed to approximate the integral with an error of…

A: Solution-

Q: 5) Approximate x²-1|dx with a right-endpoint Riemann sum using four equal subintervals.

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

Q: Use trapezoidal with 3 level romberg (k=3) to evaluate the integral from lower limit 0 to upper…

A:

Q: –1 dx x V In (-x) -3

A: Find the type of the generalized integral and examine its convergence.…

Q: Approximate the integral ∫5,1 of 1/x(dx) by Riemann sums, first using the left sum, then the right…

A:

Q: dx 3) L. Vx+1

A: Given:

Q: Find the area bounded by the curve y = x² – 6x + 5 and the x-axis from -2 to 2 using %3D Riemann…

A: area bounded by curve using Riemann sum

Q: 4) Determine whether the integral converges or diverges, and if it converges, find its value. - dx…

A:

Q: provide the steps for f(x)= sin x2/ x.     integrate using power series

A: We have to find the integrate by using poer sereis

Q: Evaluate the integral if it converges and enter the exact value. If the integral diverges, indicate…

A:

Q: 10. Determine whether the improper integral converges or diverges 3 dx (x – 1)3 -

A: Given query is to integral converges or diverges.

Q: Evaluate the definite integral: x²)dx using limit of the Riemann sum.

A: Consider the provided definite integral, ∫02 2-x2dx Evaluate the provided integration using limit of…

Q: b. It is known that on the integration interval -1 <x< 3, for the integrand function f (x): 2.2 <…

A:

Q: S°(xe* + 1)dx

A: In this question we have to solve the given integral by using some of the newton-cotes rule.

Q: Сompute f dx, where f(x)=|x|.

A:

Q: Use the previous item to determine if the improper integr 2x – x3 | dx (х — 1)2(г2 + 1) converges or…

A: Given that ∫-∞02x-x3x-12x2+1dxSolution…

Q: 19. Use Simpson's rule with n=8 to estimate the following integral. Estimate your error. So5-4 cos.x…

A: Given integral can be evaluated by using Simpson's rule with n=8 as shown below

Q: The integral of ƒ In(ln(x))dx can not be expressed as a finite sum of functions. What do we call…

A: It is called as non elementary integral

Q: 3. Express the given integral as the limit of a Riemann sum but do not evaluate: So (x³ - 6x) dx.

A: Solution:-

Q: the point of discontinuity on(0, co), the Fourier Sine integral converges to: None (**) + f(x¯)] **)…

A:

Q: At the point of discontinuity on(0, 00), the Fourier Sine integral converges to: OA None f(x+) -…

A: Here  At the point of discontinuity on  0,∞ the Fourier sine integral converges to

Q: Explain why the improper integral (x + 3) sin(x) dx L. (x² + 1)(x² + 4)² is convergent. 8

A:

Q: Determine whether the improper integral diverges or converges. Evaluate the integral if it…

A: Here given integration as I=∫2∞1xx2-4 Since ∫1xx2-a2=1asec-1xa+C

Q: .5 Estimate the middle Riemann sum for 1 dx (n= 4). 3 1-lnx

A:

Q: 1 dx is convergent x" If n>2, the integration

A:

Q: x° sin(x³) In(4 + cos(x³)) if x 10° ya. 00 Determine whether or not the improper integral dx…

A: We have to use comparison test here.

Q: Evaluate the integral if it converges and enter the exact value. If the integral diverges, indicate…

A:

Q: Find an approximation to the integral integral 0 to 4 (x 2 -3x) dxusing a Riemann sum with right…

A: Given that: The integral is ∫04 x2 - 3xdx and n = 8.

Q: 9. Use Simpson's Rule to approximate the integral f Vx3 – 1 dx withn = 6.

A: We have to find the value of given integral using Simpson's rule.

Q: An even piecewise continuous function f(x) on every finite interval of (-oo, 0) such that :/ (x)|…

A: The given statement is : An even piecewise continuous function f(x) on every finite interval of -∞,∞…

Q: 55. Show that dx J+4 converges by comparing with x³ + xdx. -3 dx. х

A:

Q: 0 In x dx converges or diverges. If Determine whether the improper integral it converges, find its…

A: Given that a integral and we find its value and check the integral diverges and converges. We know…

Q: 2. Determine if the integral converges or diverges. Part of your grade on this problem depends on…

A: Topic:- integration

Q: b) Determine whether the improper integral `1+ sin r -dx 1+x² converges or diverges.

A: Comparison test :  Suppose for x&gt;a  . If converges then also converges . If diverges then…

Q: Does fn converges to L1 and L2 i.e the distance between fn and f goes to 0

A: By the theorem: A metric  on BE is the uniform metric du  . A sequence of bounded functions fn:E→ℝ…