The sets A = {x e I: x<-1 or x> 1} then A' = [-1; 1] Ture False

Q: Suppose that T(0) = a ar average as, for n 2 0, %3D

A: (3) Given,           T(0)=a and T(1)=b and are some constant.    Define  the runing pairwise average…

Q: 1 Je* sin( t)dt 1+s* -st Prove that 2

A: We have to prove that:  ∫0∞ e-st sin(t) dt=11+s2

Q: 7. Let S = [0, 1] × [0, 1] and ƒ: S → R be defined by f(x, y) (2x³+y², 10, Show that f is integrable…

A: Follow the steps.

Q: 2. Show that by using MEAN VALUE THEOREM. u-v n >0 1+v2 3 <tan- < and deduce that 25 ww 4

A: First we have to show that v-u1+v2&lt;tan-1v-tan-1u&lt;v-u1+u2 where 0&lt;u&lt;v. Then we will show…

Q: Solve the following first-order linear DE's. y' + (cotx)y = xcscx, y = 1

A: we have to find the general solution

Q: Let f(x, y) = xcosy- y e*y. fry at (1,0)is equal to: -5 3 -1

A:

Q: Q Find the deriva tive using the de fini tion (x)

A:

Q: 7) The diameter of the base and the height of a closed right circular cylinder are measured, and…

A:

Q: 2 Exercise.8 Find: P4 (x), Pg(x), L P¾(x) P3(x) dx , LIP,(x)|² dx

A:

Q: Find the limits in Exercise

A: We know that, limx→∞sinxx=0            ⋯⋯1limx→∞ax=0            ⋯⋯2      for any constant a

Q: Prove that the following ODE IVP is well-posed: where f(t, y) = 1 + t sin(ty). y' = f(t,y), 0< t <…

A:

Q: 2 Let f (x) = x on [0, 1] Calculate x dx and x dx by dissecting O, I] oaual narts and hence show…

A: Given

Q: Let TNN(u,6²). define a faction Fact):= 2t- a, t>a, and Fact):= K (a-), tsa Find the value of a that…

A: Given:

Q: Q3: show that: S yi va -y dy =na² where a is a positive constatnt

A:

Q: x*y" + xy'+4y= 2x Ina

A: Cauchy linear differential equation

Q: Estimate the value of S, (1– x – 4r³ + 2x) dx using 4-segment Simpson's 1/3 Rule. O 2146.7 O 2315.9…

A: Numerical integration

Q: In r dy If y , then is cosh z

A: Straightway proceed to differentiate both sides,

Q: Evaluate the bound of the error if the Trapezoidal rule applied to S (x)dx . Given that 5 k is…

A: Apply formula of trapezoidal error

Q: o what does it con s conditionally conv 1. onvergence for at is the radius of approximation of e √2,

A:

Q: Let X and Y be independent and distributed as N(u, 1). Is T = X-Y sufficient?

A: According to factorization theorem, If the likelihood function L(x,θ) can be expressed in the form…

Q: 6. Given: AUVW = AXYZ Prove: UV || XY .Y W

A:

Q: what will be the valid conclusion for the given hypothesis: "f U is the midpoint of HT Then HU TU…

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

Q: Σ (X) E(Y), E(XY ) , Coν ( X, Y) , σχ, σχ and ρxΥ.

A: As per the Bartleby guildlines we have to solve first three subparts and rest can be reposted...…

Q: ==, j= 4 and x=0 about tue liney=5

A: Disk method: -  When the axis of revolution is the plane region's boundary and the cross-sectional…

Q: O Deltarentiatk with respect () Singe (X+1) (x-)

A:

Q: 3. If z = f (x, y), where x = e“ – e® and y = e® – e", show that UTM UTM az az UTM X : az - ду dx…

A:

Q: Suppose, X|0~ Binom(m.0)and e- Beta(a,B), then Var (Y) is equals to, maß

A:

Q: If fufe.- fuave diffa Veubable at'xo eI fuave difle Veubable at Xo eI Pi:I R,ists-n prove O…

A:

Q: 9 Give with an not example of T: W≤X →Y, to XT Ext. .R. boundedag. - keše bes

A: Please find the solution innext step this is an non-example of Tietze extension theorem in Topology.

Q: 28. (a) Prove that for x e R" and s < t, Ds(x) C D;(x).

A: The notation Dsx represent  an open ball of radius s, centered at x∈ℝn. Let x=x1, x2, …, xn,…

Q: (14) Approximate S, x² ex², Using Simpson's rule dp,

A: Simpson's rule is a numerical method used to approximate the definite integral which represents the…

Q: dz Find if yz – In z = x + y ax

A: To find the partial derivative of z of yz-ln z=x+y with respect x, differentiate yz-ln z=x+y, while…

Q: S 1.Prove that L (coswt) = %3D s2+w2

A:

Q: (z In z + 5)dz

A:

Q: O Find the set S on wlc fu x) = x Sin X convergas pointwise Cony

A:

Q: - seyi + avīj + () dt = 3 3

A: We have to perform integration by parts and then insert given limit

Q: J sec° (10t) tan“ (10r) dt 4 10.

A:

Q: B/let Flx)=[X]-X,x E(-2,2).which valuesof x o E(X) continuaus?

A:

Q: Q1 : prove 1 2(1–z) 3(1--z) dydxdz = 1

A:

Q: 5 Evaluate ſ“ S" r² sin ø drdøde 0,

A: Evaluate: ∫02π∫0π∫05r2sinϕdrdϕdθ

Q: Show that S ťe dt = 3VI

A:

Q: 2. Give the condition which ensure that |ez| < 1 where z in C.

A:

Q: Prove that S, pm (x)Pn(x)dx = 0 if m# n ? %3D

A:

Q: If f(x,y,z)=z In(x²ycosz), then fz is O 2z X OZ y O2z y O In(x²ycosz) - ztanz <|N

A: This question is related to partial differentiation, We will solve it using given information.

Q: 1 +y = zy" dy dr

A:

Q: Suppose that the true model is () E+ and that it satishes MR1-MR6, but you estimate by OLS (II) W=…

A: From the given information, I yi=γxi+ei The OLS estimator of γ is, γ^=∑i=1Nxiyi∑i=1Nxi2 II…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.