Determine an n so that the trapezoidal rule will approximate the integral 12 En = - 8 dx 6+x with an error En satisfying En| ≤ 0.0004. The theoretical error bound for the Trapezoid rule is given by (b - a)³ 12n² where c is some point between a and b. It predicts that the desired accuracy will be achieved if the number of terms n is at least 9.93807989

Q: Consider the error formulas. IEl s 6 - a), -[max If"(x)|], asxsb Trapezoidal Rule 12n2 (b – a)5…

A:

Q: P(−z0 < z < z0)= 0.8749 (Give the positive value of z0)

A:

Q: Use integration by parts to verify the reduction formula.

A:

Q: Consider the mid-point rule for approximating a) Derive the erTor term b) Derive composite mid-point…

A: Consider the mid-point rule on the interval [a, b] for approximating

Q: Find the z0z0 such that P(−z0<z<z0)=0.582P(−z0<z<z0)=0.582. (Round your final answer to two decimal…

A: P(−z0&lt;z&lt;z0)=0.582

Q: 11. g 13. F(r) = 3 r

A:

Q: The average number of fish per square kilometer in a lake is determined by the SDD 400xt 200 +0.2xt…

A:

Q: How large should n be to guarantee that the Trapezoidal Rule approximation to -1 (-24 x² – 10x³ -…

A: Given integral is ∫-4-1 -x4 -10x3 -24x2 -4x+4 dx Take  fx = -x4 -10x3 -24x2 -4x+4

Q: Q.3 Find the value of x, for which the geometric n series Σ(3) (x + 4)" converges.

A: Note:As per our guidelines we are supposed to answer only one question if there are multiple subpart…

Q: In5 (x + 1)²e* dx

A: Given, ∫0ln5x+12exdx  We have to evaluate the integral and simplify.

Q: 0 (x² - 1) dx b) using the Simpson Rule with n = 6. Show all work!

A:

Q: Let a) Given that In (y) can be written in the form What are the coefficients A, B, C, and D? −3x ¸…

A:

Q: Use Gauss-Legendre formula to evaluate the integral e¯x*dx_with n = 3.

A: Evaluate the integral          ∫01ex2dx using Gauss-Legendre formula with n=3.

Q: dr Find the percentage error by calculating the integral with the Trapezoidal Formula using n = 4…

A: Given that, the integral is ∫28xx2+1dx. It is known that, the formula for the trapezoidal…

Q: Integrate f(x) from x = 0 to 10 using Three-Point Gauss-Legendre Quadrature. f(x) = 5000+24563x -…

A: Given f(x)=5000+24563x-7418x2+768x3-31x4+0.14x5 Let I=∫010f(x)dx Here a=0 and b=10

Q: Evaluate the integral į (1 – x– 4x° + 2x*)cx using multiple-application trapezoidal rule with n = 2

A: Given, fx=1-x-4x3+2x5 The trapezoidal rule to approximate the area:  ∫abfxdx≈∆x2fx0+2fx1+2fx2+2fx3+.…

Q: How large should n be to guarantee that the Simpsons Rule approximation to -1 [(-2² -5 - 2 12x³…

A: ∫-5-1-x4-12x3-30x2-5x-5dx

Q: 1 qVx dx

A:

Q: Differentiate the function. h'(x) h(x) = n(x + √√x² − 3) -

A:

Q: Solve for the only positive value of x that satisfies the equation **-1 = -√(1-e-*) Using the…

A: Given that: xx-1=121-e-x Using a tolerance of 0.0001. Now solving, Let using the Bisection method,…

Q: f(x) √x 0.869in(124527.1956√x) + 0.8

A:

Q: How large should n be to guarantee that the Trapezoidal Rule approximation to -1 -5 -x¹ – 12x³ -…

A: ∫-5-1-x4-12x3-30x2-5x-5dx

Q: Suppose X ∼ Norm(0, 1). Find Var(X).

A: Suppose The PDF of the standard normal variate is written as follows:

Q: Evaluate the 6 definite integrals correct to 4 significant figures. Do not use mid-ordinate rule.…

A: