Verify by o Mathematical Induction dt todt E (2-1) = n²(2n²-1) for alt nz!

Q: Use the Error Bound to find a valve of N for which Error CSN)<1 x 10-9. is 1.5 3x

A: Error bound for Simpson's rule is defined as follows.  For a function fx, if  f4x≤M, then…

Q: Show that the series Ln=l 12+2z10n-5z"ª –3z+2;10n converges absolutely for |리 < 1.

A: The series ∑n=1∞an is absolutely convergent if the series ∑n=1∞an  Ratio test:  The series ∑n=1∞an…

Q: 5. Prove that So*(y – 0)dydr =

A:

Q: 4. Prove that for n > 0: E, 2* = 2"+1 – 1. sk3D0

A:

Q: converges, because 0 < 1 and an %3D debook 2n + 1 2n +1 2n +1 Room

A: We have to choose the true or false

Q: the book is "First Course on Fuzzy Theory and Applications"

A: To prove the inequality regarding membership function of the symmetric differenece of two fuzzy sets

Q: Let Xn ☆ Bil^,p] where n& P ae wnknown. Find method of moments estimators for n&

A:

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

A:

Q: Assume that after w months,butterfiles populace in 1000 is calculated as F(w)=12w+cos(16w)+n×100…

A: Minimum and maximum of a function depends upon all the variables present in the function.

Q: Verify by mathematical induction 1. 2(2i– 1)° = n²(2n² – 1) for all n21. 33 n(n+1) 2. Prove: Vn e…

A:

Q: 3, Re call Eudlid's proof of In finitude * primes! Shouw that T Cx): = 1{ ps X: p-pinae }12 logz…

A:

Q: Use Meithemeıtical Incluctionn to prove that for ail W with nz 2 イナ·ナ 1 1t 2-3 1 t 3-4 0-1 1 2…

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: 5.) Consider the fonction fas= x'+ex²+lx +6 Evaluat e Ho) - fc-4) 6 - (-4) fCx) di ffer entiable on…

A: Given:       f(x)=x3+6x2+11x+6

Q: (b) Prove that the improper integral ]] 8888 converges. dr dy (1 + x² + y2)3/2

A: Solution: Given improper integral, ∫-∞∞∫-∞∞dxdy1+x2+y232 As we know the convergence of the series is…

Q: Prove that Z(Sn) = {e} for n ≥ 3.

A:

Q: Give a recursive definition (with initial condition(s)) of (an) where (n = 1, 2, 3, . . . )

A: We have, an = 212nWe have to find a recursive definition with initial conditions of an starting from…

Q: Compute 32+n21-3n n=0 If this is divergent, input "O" as your answer If applicable, submit answers…

A:

Q: he IIIT-Delhi robotics club has organized a Robothon. n robots are placed along the edge of a…

A: Now we can see that the maximum money the club might end up spending is the maximum of the two…

Q: Prove that. 2/nJn-(n+2)Jne2 + (n+yjJney --- 3. end hence deduce that. 1xJn - (nti)Jnas -…

A:

Q: it is unbaised estimated of a Then Show That ta is baised estimated of O2.

A:

Q: IRI- 2. <| sinz|< -e 2

A:

Q: Is 7/4 In(secv) 2t 1 e* dx dt dv = 2 8 - 00 (don't change the integral sequence) O True O False

A: Using the limit

Q: Consider ax with the given coefficients a,: (2x)" n = 1 ind the radius of convergence R.

A: In this question we will use basic of calculus i.e concept of infinite series. We will use ratio…

Q: The only particular solution to a second-order linear homogeneous ODE is the zero molution. elect…

A:

Q: *show tht the fanetion fW=$- satify The by PotheseI of Rolshe oren- on [0,4]

A: For the solution follow the next step.

Q: 10. Show that S t2 if 0 1, 2(1 - e-) then Ldf %3D

A: Laplace of differential equation.

Q: 1. Prove that L(t)=. 1 s2

A:

Q: Find Š Clim sup and s Clim inf) nt (-1) (znt) of Sn=

A:

Q: Suppose {fn}n=1 converges uniformly on E. Show {fn}n=1 converges pointwise on E.

A:

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

A:

Q: Determine Z- Trans furm in cludig vegiva of con vergence in n 7o メ(At n<o

A:

Q: Q-5 Consider NLP problem, max 8() --2+ 2ィ-ズメューメュ+1 ダ」ン0 ズェン」 19 (2). Satsty fnst1 2nd order. For ist…

A: Given: Let's consider the NLP problem max sx=-x12+2x1-x1x2-x2+1 subject to x1≥0x2≥1,xa=12,1  satisfy…

Q: Find Residues by using Lourent's Series f(²)=3/²2 at Z₂ = FL

A: Given f(z) = zz2 - 1

Q: 4-5. Evaluate the Integral 31) dt

A:

Q: 4n2 Tantel show whether (an )Cconverge diverge or

A: Given : The given series is :  ∑n=1∞un= ∑n=1∞4n29n4+1. To find : We have to find whether the given…

Q: What is the net crarop for fW={+5,05 as we qo from x=2 to X=5?

A: The given function  f(x) = x2 + 5

Q: 8. Use the integral test to determine if IM8 k² (k³ + 2)3/2 converges.

A:

Q: Use Simpson's Rule with n = 4 to evaluate [² (t³ + t) dt

A:

Q: Show that S ťe dt = 3VI

A:

Q: Calculate Sxe 0 re-L₂ (x)L(x)dr by using Recurrence relation of Laguerre function, Ln

A:

Q: s defined over ai at one point in tl асcordi

A:

Q: Set n n and K intgers 1SKE ni Shorw that 2n42 2 - 2n %3D K-I Kニ)

A: Binomial Theorem: According to the binomial theorem, let x and y are any two numbers. Then it is…

Q: 3)suppose fle) isadifferentialle fmehon on the intervall E-7,J Such that Hl-7) =4 and fl)=1.…

A: Intermediate value theorem

Q: Suppose / (s) - (÷)*" valuate: Js(x) dr +C 3- In (5)

A: Given      f(x) = 1512-3x

Q: 1 i. Use the result in (i) to test for convergence 2n =1 2 Vn? +5

A: See the attachment

Q: 7) Show that K± = det [ T 4 J.

A: Sol