If S= 1+3+5+7+9+11+... + 99, then 49 s-Σα r=0 where a,

Q: ds if s = Find dt 7t + 3 ds dt II

A: We have given;

Q: 23. Given that 4sinh - 2coshx = Ae*+ Be* then A and B are respectively А. 1,-3 C. -1,-3 В. -1,3 D.…

A: Topic- trigonometry

Q: Let S = {:n e N}. a) Show that inf S exists Question 16 %3D b) Show that inf S = 0

A: PART A The given set is : S=1n:n∈ℕ As we know that : ℕ=1,2,3,4,......... The set is given by :…

Q: 3). wh.ch of these condition ally Ca uvergent! Tuere may be more than 1 right answer. Odre arctan u…

A:

Q: 1. w = sena cos ß 2. W = w u+v 3. f(r,s) = rln(r² + s²)

A: w = senα cosβw is the function of α and βFirst partial derivatives : ∂w∂α = cosα cosβ     {β will be…

Q: If F (s) = then %3D (s+1)2+4

A: Using inverse transform properties, f(t) is given.

Q: If сх 3D су (тod n) and c >0 then а) х 3Dу (тоd сп) Ь) х%3D у (тod n) с) хну (тod") а) None of thes-

A: We have to solve given problem:

Q: 2.16 If S = {r |0<< 12}, M = {x | 1 < z < 9}, and N = {r | 0<r<5}, find (a) MUN; (b) MON; (c) M'nN'.…

A:

Q: 2en cos 2t 2s s2 + 4 O option 1 None of the choices s + 2 s2 – 2

A:

Q: 0 0 0 3 0 0 0 2 0 0 0 4 -1 C = 0 0 0 -2 det C = [C] If a1, a2 and az are given show that af az az 1…

A: C=-100000300000200000400000-2A=1a1a121a2a221a3a32

Q: 1) Suppose A e M„(R) is. show: A) A is singular if and only if adj (A) is singular. n-1 B) If n > 1,…

A: The solution is given as

Q: 1. Given s=6x720: Find a) whure y is at eauilibriuma is increosing <) whe y is docieosing 5) where

A: Given y'=6x2+7x-20 So, equilibrium of y will exist where y'=0…

Q: (d) The apartment is hot if and only if the temperature is not 75º and the air conditioning is not…

A: Here given Statement in English convert them to symbolic form using standard notation

Q: Find a formula for sn, n > 1, if s, is given by 2 3 4 6 - - - 3' 5'7' 9 ' 11

A: We have to find Sn

Q: 2- Let z=x+iy. Find a) Img(1/2) b) Re z c) Img (1/z')

A:

Q: .3 If U = 2 – x, | x/2- xdx= = n} .3 -J uvūdu В (2 – u)/ūdu | .3 © (2- u)/ūdu 1 (D uvūdu A)

A:

Q: 1 -dr. a In r| Find 3.

A: Let's find.

Q: 1)z = e(4+j3) In(6230") 2) z = (-;)(* 2) z = (-)(r)"

A: (1) The  given complex equation is                                                Z=e4+j3ln6∠30°

Q: Let P = {p:p=6x-1, for some x EZ} and Q= {q:6y+5, for some y EZ). Prove that P= Q

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Q: /et A 3 8 カー (-45 Show That LA+B S ZA+B) 3-5 = At B

A: Transpose of a Matrix is defined as “A Matrix which is formed by turning all the rows of a given…

Q: Suppose, X0- Binom(m,0)and 0~ Beta(a, B), then E(X) is equals to, a) maß b) aß ma c) d) me

A: Given: Suppose,  Xθ~Binom(m,θ) and θ~Beta(α,β)

Q: If e'z = /3 -i.Then Im (z) is %3D O a. e2 b. 0 С. 1 d. -In(2)

A: eiz=3-i Now let z=x+iy. Then, ⇒eix+iy=3-i⇒eix+i2y=3-i⇒eix-y=3-i…

Q: Given: RQ = TP ZQ = ZP Prove: RZ = TZ

A: Given: RQ=TP, ZQ=ZP According to given figure RQ=ZQ+RZ…

Q: (b) If m < a1 + ... + an < M n, and v, is positive and + anVn < Mv1. + anUn| < Mvi Vn. decreasing,…

A:

Q: Find an explicit formula for s, if so = 1 and %3D Sn =2+2s0 + 2s1 +... +2s, 2+ Sn-1, Vn >1.

A: Generating Functions for a sequence a0, a1,a2,………an,……………… is an infinite series of the form ,…

Q: Determine if the following is a fundemental set of solutions to  y'' -6y' + 25 = 0 Given that…

A: If the Wronskian of two solutions is not equal to zero, then the given set of solution is…

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

A:

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: 5. (BH) Calculate det B, where 0. 4 1 1 В — 1 -2 4 -1 2 1 -1 0 7

A:

Q: The number of the element(s) of order 17 in Z17 O Z17 288 16 17 None of them 289

A:

Q: What is the general solution of (* + s) dr + s² (3r + ks ) ds 0 where k is a constat 4rs + r + ks' C…

A:

Q: Let w = z. In(xy² z®), then which of the following is- O a. O b. O d. O e. 0

A: While finding the partial derivative of a multivariable function, if we have to find the partial…

Q: S. ADEF with N-2,-1), -1, 3). 6ARCD with A(I, 4), R3, 2), CO, -2). FO. -1) in the sasis D-3, 1) in…

A: #5  Reflect the triangle DEF in x axis  For reflection over x axis , the rule is  (x,y) -----&gt;…

Q: Let a = 8 and b = 9. Find m,n E Z such that am+bn =1.

A:

Q: 4 Let w = x. In(xy²z³), then which of the following is O a. 0 O b. O d. O e

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Q: A := {x € (0,1)|x= ar, for some r € Q} re that sup(A) = 1.

A:

Q: Show that if X gamma(r, A) and Y ~ gamma(s, ) independent, are then X + Y is gamma(r + s, ).

A: X~Gammar,λ fx=λrΓre-λxxr-1,     x&gt;0, r&gt;0, λ&gt;0 Y~Gammas,λ fy=λsΓse-λyys-1,     y&gt;0,…

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

A: Laplace of differential equation.

Q: 10.B.4: Suppose TE£(V) andcEF. Prove that det (cT) = cdim V det T.

A: Here given that T∈L(V),is the set of linear maps from V to V.

Q: 6-1718 ss (a) For t= 1.735, should you reject or fail to reject the null hypothesis? prary O A.…

A:

Q: 9°c2 S = 1+ 9°c + 2! 9°c3 912c4 Let +..... 3! 4! If In S = 17496, then find c. 9°c2 9°c3 9124…

A: Proceed as shown below...

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

A: Evaluate: ∫02π∫0π∫05r2sinϕdrdϕdθ

Q: al solution of - uy = 0 is O is *+c,e¯*)(c

A:

Q: If сx 3D су (тod n) and c >0 then а) х%3D у (тоd cn) b) х%3D у (тod n) c) x = y (mod“) d) None of…

A: We have to solve given problem:

Q: Write equation for each ellipse

A:

Q: EVALUATE S(3sin t - 2cos t) dt

A: Topic = Integration

Q: 7) Show that K± = det [ T 4 J.

A: Sol

Q: Let P= (p:p=6x-1, for some x EZ) and Q = {q:q=6y+5, for some y EZ}. Prove that P=Q

A: