(5) Let' (1) : r² + 7x + 12. S(z) dr (a) Use a comparison test to show that. A B converges. S(x) (b) Find A and B so that r +3' a+ 4, As always, show all your work. (c) Find. S(x) dx /1

Q: sin N 8) Show that converges/diverges.

A:

Q: 1. f is increasing on the intervals 2. f is decreasing on the intervals 3. The relative maxima off…

A:

Q: p for which In (n) Comvenges

A: Given∑n=1∞ln(n)np

Q: Which of the following information is correct for the sequence 3 dx 1 dx 1 dx dx {an}n=1 | 5. 7. (a)…

A:

Q: Start with an initial guess x = a₁. Then define a2 to be the x-intercept of the tangent of f(x) at…

A:

Q: What is the convergency interval of (-1)"-_(*-2)* 3-(2n+1) {(-)

A:

Q: If 2 a, is convergent with positive terms n=1 is it true that sin (a,) is also n=1 convergent?…

A:

Q: WNII sin 2 7) Show that 4 VN converges/diverges.

A:

Q: 18 For which numbers a does x,+, = a{x,– x) converge to x* = (a – 1)/a?

A:

Q: 5. Consider the equation f(x) = x - 2- = 0. (a) Show that the above equation has a solution on the…

A:

Q: „(4 - 1) = "p : И

A:

Q: 00 Se*dx Find

A:

Q: Suppose that an(x – 6)" converges for x = 10. At which of the points (a)-(d) must it also converge?…

A: Given: The given series is ∑an(x-6)n  The series converges at x=10. According to theorem is the…

Q: 1² + 11 For what value(s) of n, the integral dr converges? Justify In + 8x2 + 2 your answer.

A:

Q: V2+cos (n2+1) Use the basic comparison test to determine whether E1 n=D1 converges or n+en diverges.

A: To check the Convergency of the given series. We apply here Simple comparison Test and Ratio Test of…

Q: An+1 Suppose limn→∞ = 3. Find the radius of convergence of 8. An an(-1)" En=0 -(x – 8)" ? 2"5

A: To find the radius of convergence of the given series

Q: 00 4" converges or diverges. (9n)2 t) Use the ratio test to determine whether> n=6 d the ratio of…

A: We have to use Ratio Test first.

Q: +9 for all n2 1. Prove that {r,} converges and find 2.1 4. (a) Let r = 4 and am+1 its limit.

A: Sometimes, a sequence is defined recursively. In that case, to test the convergence of the sequence,…

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: Q(3) The sequence 4n3 3n7 + n3 2n7 (a) Converges to (b) Diverges (c) Converges to

A:

Q: lim (n22n) / n! = ?

A:

Q: (k + 1)/2 (k5 + k3 – 1)/3 1. Show that converges. k=1

A:

Q: Which of the following information is correct for the sequence 7. 9. dx 1 dx 1 dx 1 dx {an}n=l 5 (a)…

A:

Q: Verify that x = 1/a is a fixed point of the function g(x) x(2 ax). Determine the order of…

A: To show that x = a is a fixed point of g(x)=x( 2-a x) it is sufficient to show g(a)=aand if we can…

Q: Let ∫∞−∞ f(x) dx be convergent and let a and b be real numbers where a ≠ b. Show that

A: Let ∫-∞∞f(x)dx is convergent and a,b∈-∞,∞ To Show: ∫-∞af(x)dx+∫a∞f(x)dx=∫-∞bf(x)dx+∫c∞f(x)dx     If…