.Prove that e- -dt < (1+ t²)* 1/4 6.

Q: 2. Determine if S dx is convergent or divergent. x²-x

A: In this question we have to determine if this integral convergent or divergent. If limits exists…

Q: 2. Let {N(t),t 2 0} be a renewal process and (X,,X,, X,.-be the corresponding interarrival times.…

A: A renewal process is a stochastic model that occurs at random and is temporal based. The process…

Q: If the moment-generating function of X is M(t)= e, then the moment-generating 3t function of Y=1+-X…

A:

Q: 1 (x + 1)2 dx -2

A:

Q: Theorem 1.7.4 x" -le* dx is convergent if and only if n> 0.

A:

Q: 1 is not convergent. Theorem 1.8.2 E n = 1

A:

Q: If L(x)=mx+b is the linearization of f(x)=2x³ - x +3 at x-1, then m= Using L to approximate 2(1.01)…

A:

Q: (4) The general solution to 7xy" – y + 10y = 0 is y = A x + x+ x²+ x3 + ... -) +В х x²+ x³ + + x+…

A:

Q: 3.3 Prove that does not converge uniformly on R. k! k=0

A:

Q: Show that >n"x" diverges for all x + 0. n=0

A:

Q: 1. Show (in terms of e – 6) that a function f : [2, 7] → R be defined by f(x) = Vx² + 1 is uniformly…

A:

Q: 7) Use Theorem 7.1.1 (Table) to find L{f(1}} for the following: S)-(e*-e*)}° a.

A: The given function is f(t)=(e-3t-e5t)2. Expand the function implies, f(t)=e-6t+e10t-2e2t The Laplace…

Q: Σ does not converge uniformly on R. k! k=0 Prove that

A: We know that ∑k=0∞xkk!=ex. So, we will show that ex does not converge uniformly on ℝ.  Let us assume…

Q: 5. Let fn(x) ". Show that z"0 uniformly on (0, ).

A: We have to use squeeze theorem here.

Q: 2. Estimate the largest value of x that allows e* to be approximated to 0.01% accuracy by the…

A:

Q: Find all values of x for which ) (3x)" converges. n=D1

A:

Q: Find an example of fn → f in measure, but for every x, fn(x) does not converge to f(x).

A: We have to find an example of fn→f in measure, but for every x, fn(x) does not converge to f(x).

Q: 1/x e 7 dx y3 -1

A:

Q: Find the best rank 2 approximation to A from (1) with respect to ||:||F.

A:

Q: 1+ By using the definition In(1+x) = / 1 -dt, show that for a certain range of values of r, t…

A: Solution:

Q: 1. Show (in terms of e- 6) that a function f : R + R defined by f(1. y. 2) = (2x + 3y + 42) is…

A:

Q: (a) Prove that (2x + 2) > 1 for all x > 0. (b) Let so > 0, and sn+1= } (2s, + ) for all n > 0. Prove…

A:

Q: Suppose that T(X) is sufficient for 0 and that ^e(X) is an MLE of 0. Show that ^0 depends on X…

A:

Q: Find the interval of convergence of E(-1)". n 2n 36" n=0

A:

Q: Show (in terms of e - 6) that a function f : [2,7] R be defined by f(z) = V² +1 is uniformly…

A: In this question, we need to show the given function f(x) is uniformly continuous.…

Q: Show that the series n=0 xn cos(nx) x² +n³ + 1 defines a differentiable function g(x) for x in [-1,…

A:

Q: Discuss the Convergence or Divergence for D { [4+ (-0"]" (Z+2)" こう 2n+1 - DZ² 2 لع Wi ngo (2n+¹)!

A:

Q: If Σ α An diverges then E ca can diverges only if c > 0 only if c < 0 only if c+ 0 for any real…

A: Given, ∑an diverges then find for which values of c, ∑can diverges.

Q: Find the interval of convergence of E 27" (x – 7)3n+2 n=0

A:

Q: Determine if the given is convergent or divergent. (x²+1)² n Zn=1 (n²+1)²

A:

Q: sin(²) En=1 is 18 √n a. 1 b. 12/12 c. Converge d. Diverge d O C O a O b O

A:

Q: 11. Suppose f and g are continuous positive functions. Provide an example such that diverges and…

A: We need to provide example for convergence.

Q: 2 Let xk = E(k+1)(k+2) for all k e N and define S, = Ek=1 ®k• (a) Evaluate Sn as a function of n.

A:

Q: -press the integrand as a sum of partial fractions and evaluate th dx 4) S= x2(x2 - 16)

A: Solution of the problem as follows

Q: Find the interval of convergence of E n(x – 8)" n=2

A:

Q: Show by example that E=1a,b, may diverge even if E=1an and E=1b, both converge.

A: According to the ratio test, determine the value of limit. If L&lt;1, the series is convergent. If…

Q: Derive the moment generating function of X ~ Bi(n, p) and using the MGF compute E[X] and Var[X].

A:

Q: 2.44 Suppose f is uniformly continuous on D and suppose E c D. Prove: f is uniformly continuous on E…

A:

Q: Prove with an e – N argument that {fn(x) + gn(x)} converges uniformly to f (x) + g(x) on R.

A: The objective here is to prove that : fnx+gnx converges uniformly to fx+gx Given: fnxconverges…

Q: (h) (3x)* (3.r)* 2k |1 k=1

A:

Q: determine the radius and convergence of E n=1 5xn/3n2

A:

Q: There is no value of r such that Jo (3t)-r 5 dt converges. 14.

A:

Q: 1.3 write the fallowing integral (a) e | Determine whether the folawir Converges or diverges. x- 3x°…

A:

Q: 15: Let 8(x) = ,10/t dt 2/x %3D Find g'(In 6). 15552 (A) (In 6)2 15552 (B) (In 6)2 - e$/2 15552 (C)…

A:

Q: -B/ls//E-x] in (6.14) is distributed as at =

A:

Q: Suppose f and g are continuous functions. Provide an example such that | g(x)dr diverges 0. adf(x)dr…

A: Follow next step

Q: Find the derivative of following series: (k + 2) 2k k+1 a) OE (k + 1) (k + 2) 2k k 1 b) OE (k + 2)…

A:

Q: If f(x) > g(x) >0 for X in [1,0) and g(x) dx diverges to +0, then | F(x)dx also diverges to +. True…

A: It is TRUE, that 0&lt;g(x)≤f(x) for x in [1,∞)  and                               ∫1∞g(x)dx diverges…

Q: Which of the following graphs is the slope field for dx 12 -3-211. s 2 13 US 111-2-/35 1112 111²-111…

A: Here we have to solve the given differential equation and plot the solution

Q: 1. Use the Gauss forward formula with xo = 2.0,h = 0.15, n = 7 to find an estimate for f(2.5) if %3D…

A: Given: fx=xlnx. x0=2.0, h=0.15, n=7.   We can solve this by using Gauss forward formula