3.9. (a). Prove that z is either real or purely imaginary if and only if (2)2 = 22. (b). Prove that v2|2| > |Re z|+ |Im z|. %3D

Q: Q3: Prove that Σ(y₁ - y) = 0 AND Σfi(y₁ - y) = 0

A: The question is about proving given equation. To prove : ∑ ( yi - y¯ ) = 0∑ fi ( yi - y¯ ) = 0

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: 2. Consider the following quadratic form; F(x,y) = ax? +2bxy + cy. Examine under which conditions on…

A:

Q: 6. Prove that for x > -1 then Vn E N, (1 + x)" >1+ nx .

A:

Q: 1.2.10 1 if x < a, f (x) = 2a elsewhere on (-T,"|, where 0 < a < T. Sketch for two different choices…

A: Since, you have post multiple question here. I am answering first one. Please post again with…

Q: 5. Recall that we defined In r S4. for r> 0. Prove that In(ry) = In(r) + In(y) for all r, y > 0. (*)…

A:

Q: Suppose f" (x) = N,(h) + a,h? + azh* + azhº + ... %3D The value of N2(h) using Richardson's…

A:

Q: 4. Define f: [0, 1] → R by if x E Qn [0, 1] if x ¢ Qn [0, 1] f(x) = (a) Prove that S° f = 0; s*f =…

A:

Q: for which the sys y +z = 6, 4x + Ay = -5 has infinitely m a root of which qu: %D :

A:

Q: 2. If z = x° In 2.xy, find at 1,-

A:

Q: s(2) f(z) is analytic in C

A: Ans : false

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: 10 a- Let X1, X2, ..,Xn~N(0,0) and T Find %3D X2 E (T),Var (T)

A:

Q: .(1) t is straightforward to show that y = k-1 is a solution to the homog quation

A: Given,                yk+2 -2k+1kyk+1+ kk-1yk=0         (3.151)and       yk+2 -2k+1kyk+1+…

Q: Prove that for the gamma function [(x) = ftx-¹e-tdt that for n a positive integer then I(n) = (n-1)!

A:

Q: Let f(t,y) = y+ 3t?e'. Then f satisfies a Lipschitz condition in y with L = 2, given that 1sts2.…

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

Q: Which of the following is the statement of Fermat's Theorem? O a. lf f(c) exists and f(c)=0 then, f…

A: Fermat's Theorem: Fermat's Theorem is explained as if fx has a local maximum or minimum at x=c and…

Q: S Prove that L(cos 3t) : %3D (s2+9)

A: We know that Lf(t) = ∫0∞e-stf(t) dt Then Lcos 3t = ∫0∞e-st cos 3t dt                             (1)…

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: 1. Find the interval(s) wheref(x) = xe6* is concave down, if such an interval exists.

A:

Q: -2 Let f(t,y) = y + 3t?e'. Then f satisfies a Lipschitz condition in y with L = 2, given that 1<t<2.…

A:

Q: 1 1 Prove that: L' a exp(a't) erfe( avt), where erfc is complementary a+v error function.

A: Formula Used:- L1t=πsLeat=1s-aLerf(at)=as(s+a)Leatf(t)=F(s-a)                   where…

Q: 2/3 Determine the length of x=| for 0<ys2. Assume that y is positive.

A:

Q: S Prove that L(cos 3t) (s²+9)

A: Given L(cos3t)

Q: Find solution of an equation x X f(x) 1 1.0000 1.25 0.8000 1.50 0.6667 0.5714 1.75 2.0 0.5000 Using…

A:

Q: In(1+2x) Find the Padé approximation R1,2(x) for f(r) %3D

A:

Q: 4. Evaluate both sides of Green's theorem, for: F = (-x²y,xy²) where C is shown in the following…

A:

Q: 2. and XR %3D C. Two tails with n = 34 , x =

A: Solution: From the given information, level of significance is 0.01 and n=34.

Q: 1. Differentiate the following with respect to x: a. y= 5x - + 5Vx + 3p ex + In(x) - 7 (9)

A:

Q: 3.Eliminate the arbitrary constant on the given equation: xsiny – x²y- C

A:

Q: Q4 Prove that E(",") = ("::)- () .n 2mzr. %3D +1 +1

A: we have to prove that                                                   ∑k=0mn-kr=n+1r+1-n-mr+1 now,…

Q: Show that g(t) = t2tant takes on the value ½ for some t in [ 0 , π/4 ].

A: gt=t2tant on the interval 0, π4. When t=0, g0=02tan0=0 When t=π4, gπ4=π42tanπ4=π2161=π216=0.6168

Q: 1d. Show that the given equation x- In xX= 0, has a root in the interval [4, 5].

A:

Q: 42) Find the aritical mumbers of the function. gle)= S-x²

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: 6. so be it r = 3xi + yi – 2zk and f (r) : -- where |r| = r find all of grad(f) and div (-)

A:

Q: 2. Let G = Z,xZ4, and find [G:H] for: a) H = {0}xZ4. %3D

A: We have to find [G:H]

Q: Suppose f"(x) = N (h) + a,h + azh2 + azh + -. The value of N½(h) using Richardson's extrapolation…

A:

Q: 7. Prove that if v >-1/2 ; p) = L{xvJ, (; = xı-at-a) H

A:

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

A:

Q: 1. Let s, =2+j8 md -, = 4+j36. Show that a. -1+- = -+- 1 -1- -2 -1 -2 = -1-2 -1 : b. C d. =2 ||

A:

Q: 2 2 2 1+ 2 t3十 Cn)和 9 Prove that

A:

Q: Suppose f(x) = N(h) + a,h2 + azh + agh +.. %3D The value of N,(h) using Richardson's extrapolation…

A:

Q: Find fCx) if flo)=0 and the tanGat (k,F CX) has ine af Slore x(x+2) a

A: Given for the function F(x), F(0)=0 and tangent line to F(x) at x,F(x) has slope xx2+23.

Q: Ex. Save the following sef of Lincar equations using with R=11 over relaxation 10X, +X2 +X3 12 X, +…

A: In numerical linear algebra, the method of successive over-relaxation (SOR) is a variant of the…

Q: x+1 Q1/ Prove that coth-1x = x-

A:

Q: Ivy is not sure whether a particular c the coin is not fair if she observes 4 4.24 and alternative…

A: Ans:

Q: D Reduce the Q.F 22,xz t 22,X3 2ズュズ3 weag ayf of oothogonal toans fermation by an Ans: y+92-295

A:

Q: Let flt.v) = v+3t°e'. -2 -y + 3t2e'. Then f satisfies a Lipschitz condition in y with L = 2, given…

A:

Q: 3. If f(x) = -x, g(x) = 2x + 1 and h(x) = x2, find fogoh 1 point %3D %3D О А. х2 - 1 О в. 2х2 - 1 О…

A: We use fogoh=f(g(h(x))).