1 (a) Use the Integral Test to show that > converges. 2. n' +1 d 1 n = 0 -1 tan dx Hint: 1+x?

Q: allsweCI -5e" dx converges 4x to

A:

Q: solve integral eqn. use L.T. and Convolution Integration 0 to t ( y(x)/(sqrt(t-x)))= 1+t+t^2

A:

Q: The improper integral -dx is (x+2)® 1 converges to O Diverges converges to converges to converges to…

A: ∫-1∞1x+295dx=∫-1∞x+2-95dx                                =-541x+245-1∞…

Q: 6. The improper integral dx converges to /x- 5 '5 Vr-5

A: The given integral is an improper integral of second kind.

Q: Is the integral [_(0) ^(5) x/(x² − 16) dx convergent? If so, what does it converge to?

A: Given that the integral ∫05xx2-16dx. Check the convergence of the given integral and if it…

Q: Use the to Series integral test whe ther the de termine -15 convergent or divergent n.Ln(n) n=2

A: The given series is ∑n=2∞5n.lnn

Q: The values of a that make the integral Tdx converges

A:

Q: What is the radius of convergence (x-4)" Ση=1 n m

A: Given

Q: sin (xy). In x dx Finding the uniform convergence of the integral

A: Given: ∫01sinxylnxxdx, y≤1 By using the infinite series expansion of  sinθ=∑n=0∞-1n2n+1ǃθ2n+1, the…

Q: If the improper integral always TRUE? P P - Op=1 P 3 2 V 3 2 32 So ve Op < 1 de converges, then…

A:

Q: Determine whether the following series is convergent or divergent 3- Vn ( a) Σ Vn3 n=1

A:

Q: 5. S sin(3 ln x) X dx

A: Need to find out the integration.

Q: Evaluate this Type II improper integral; if convergent, find its’ value. integral upper=pi/2…

A: secx-tanx is not defined at x=pi/2. Therefore, given improper integral can be written as We know…

Q: Use the Comparison Test to determine for what values of p the integral 1 dx converges. хР In(x) (Use…

A: Given integral is ∫3∞1xplnxdx

Q: n.Sin (t Converges or diverger

A:

Q: Determine whether the following integral converges or diverges. Be sure to use proper mathematical…

A: We have to check the given interval is convergent or divergent.

Q: The improper integral 1 dx converges to '5 Vx-5

A:

Q: If 2 Cnx" is convergent when x=2 and divergent when x=-3, then 2 Cn is n=0 n =0 convergent. O…

A: Consider the given information: The series ∑n=0∞Cnxn is convergent when x=2 and divergent when x=-3.…

Q: 5. Determine if the following integral is convergent or divergent. Do not calculate it. 1+2 sin(¹)…

A:

Q: x° +4 Perform a test to determine if dx converges. X' x° +4 Does -dx converge or diverge? O Diverge…

A: An improper integral is a type of integration that determines the area between a curve.