Which of the following is true of 18 Select the correct answer below: 13 1 O The integral converges to The integral converges to 0. 1 4(5)4 The integral converges to The integral diverges. 1 -4(5)4 (x-8)5 dx?
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- 6). Use the Integral Test to determine whether the sum converges. ∞ n = 1 1 n + 8 Evaluate the following integral. ∞ 1 x + 8 dx 1 Since the integral is or is not , divergent, convergent or incocluisve ? please show step by step please10. Use the Integral Test to determine whether the sum converges. ∞ n = 1 n 9 + n2 Evaluate the following integral. ∞ x 9 + x2 dx 1 Since the integral finite, . PLEASE SHOW STEP BY STEP CLEALRY11. Use the Integral Test to determine whether the sum converges. ∞ n = 1 6n 1 + n4 Evaluate the following integral. ∞ 6x 1 + x4 dx 1 Since the integral is or is not , .infinite converegent , divergent or incoclusive . please show step by step clealry
- For which a does 1/n(ln(n))^a converges? Justify your answer.Suppose that Newton’s method is applied to find the solution p = 0 ofthe equation e^x − 1 − x −1/2x^2 = 0. It is known that, starting with any p0 > 0, the sequence {pn} produced by the Newton’s method is monotonically decreasing (i.e., p0 > p1 > p2 > · · ·) and converges to 0.Prove that {pn} converges to 0 linearly with rate 2/3. (hint: use L’Hospital rule repeatedly. )Represent the function 2/(1−10x) as a power series f(x)=∑n=0∞ cnxn C0= C1= C2= C3= C4= Find the radius of convergence R=
- Solvef(x) =x2−xcos(x) +14−sin2(x)4= 0,withx0=π2.(1) Does Newton’s method converge quadratically to the rootr=r1∈[0,1]? If not, explain why?(2) Find the multiplicity of the rootr=r1off(x).(3) Write out the Modified Newton’s Method such that we havequadratical convergence.Q2. (a) Find an expression for y including first six derivatives in the series, giventhat y'=0.1(x3+y2), subject to the initial condition y (0) =1.(b) Given the ODE, y'=y-x/y+x, subject to initial condition y(0)=1. Use the classicRunge-Kutta method to solve the problem in the range 0<x< 0.5, taking h=0.1.