). Show that Vーu リーl < tan vーtan if 0

Q: Prove that ||A||1 = maxi<j<n{E#1 laij|}. i=1

A:

Q: a Prove that < 16 – a| for each a, b e R. - V62 + 1 Va? + 1

A:

Q: =[12] and U- = -[] Then A2017U is equal to -1 Let A =

A:

Q: If I, = [x^tan"x dx, Prove that (n+1), + (n-1),,2 ° п 1 %3D 2 n

A:

Q: Prove that tr(aA + bB) = atr(A) + b tr(B) for any A, B belongs to Mn× n(F).

A: We need to prove that tr(a A + b B) = a tr(A) + b tr(B) for any A, B belongs to Mn×n(F).

Q: 31 30 Find a mat rixP such that PT 0 2 0 2 1 1 = %3D 0 1 AO 1 0 1BO -1 0] P = 1 1C 1 -1 1 DO P = %D…

A:

Q: 2. Which piece of information is necessary to use the SSS Congruence Postulate to prove that ATRY Y…

A: Which piece of information is necessary to use the SSS Congruence Postulate to prove that ΔTRY≅ΔCAP,…

Q: prove that 01a| = 0 => a=o @ 1-al-lal @lak b ⇒-b<a<b @la-bla lal-lb/

A:

Q: 4. Let I and J be ideals of R. Prove that ifINJ={0}, then rs = 0 when reI and s eJ. %3D

A: Given that R be a Ring snd I.J be two ideals of R .Let r∈I and S∈ISince , r be an ideal and S∈J≤R…

Q: Prove that ((¬(p → r)) ≡ (r → p)) is a wff.

A: We have to solve given problem:

Q: 4\ let ü = 31 – 2j – k, v = -i +j-k, w=41-2j + 3k And find u x (vx w) ?

A:

Q: Prove this! P (an) = W/ NM) [M-N (p-q)" ] 8 Npq %3D exp

A: your question is not clear i think some error in the question plz confirm it.....

Q: Show that J74) LOSK +Sinn 2. %3D TIX

A:

Q: Show that the finite difference formula 1 Dzu(î) = [Зи (т) — 4u(г — h) + u(т — 2h)] 2h is a…

A:

Q: Prove that 12) d SIAX 13)let y=x, find Ay/Ax

A: Derivative of function

Q: Let j = 7 and U=span(ü), with ü = -6. Write j = ã1+ã2, where 1 in U and az in U-.

A:

Q: 6. Let a, b e Rwith b + 0. Show that R(a + bi) = C. %3D

A: We have to show that R(a+bi)=C. We prove it in two oashow that R(a+bi) is a subset of C and C is a…

Q: Prove that i 224 s 2xP for xzO, y zo i and 1 t L-l with p>

A: Given that x,y≥0. And 1p+1q=1 with p&gt;1. Consider gx=xpp+1q-x. Then g'x=xp-1-1 and g'x&lt;0 when…

Q: 3) Use the Second Principle of Finite I nduction to establish that for all nz I o"-1= (a-1) Co to ta…

A:

Q: Let x, y E Z. Prove that if 3 ł x and 3 ł y, then 3|(2² – v²).

A:

Q: Show that the intervals S [1,3] and T =[2,8] are equinumerous by finding a. bijection between them.

A:

Q: If A' = g;a,rsys , Yi = birx, , and a;,b,j = dij. Find A' in terms of the x,

A:

Q: Let a = : 3432, and b = 332. Find x, y € Z such that xa+yb = gcd(a, b). To get full marks you must…

A:

Q: Find all the values of x in the interval [0,2pi], that satisfy the question.  10cos(x)+5sin(2x)=0

A: Given equation is Solve the given equation for x

Q: Show that the following cosh 3 (0,0) r(3,5) x² y?. (10xdx +6ydy)

A:

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

A:

Q: Let linear tiansformation I(4)=(2,32and Tls0) =(3B,2) Cheek whether T? exists or noti2 Find T. E=R…

A: The objective is to check whether inverse of T exists or not and find it.

Q: If u, v are given unequal numbers anu (un-1+ Pn-1), vn = V (u –1 Vn-1), where n2 2 , %3D Un %3D 2…

A: Given

Q: of af 42. Assume that w = (х, у) — ху, and (х, у) ду dw dw Find and at ds

A:

Q: Consider (Ru) .f : R->R -3 X3o 3. X70 Prove Pex) is Con tinuos onR-301

A: Given that                                      f:R→Rf(x)=-3; x≤03    ; x&gt;0 we have to prove that…

Q: (a) Let r(t) = ti+tej+fk. Find ((1),4 × (?),1) - (1)a tuj

A: First we find out first derivative of r(t) with respect to 't' then find out 2nd derivative and then…

Q: 3. Consider tw o evénts A and B such that Pr(A)= 1/3 and Pr(B)= 1,2. Determine the value of Pr(B 0A)…

A: Given PrA=13 and PrB=12 and A and B are disjoint, that means PrA∩B=PrA×PrB…

Q: Show that (t As) can be derived from the premises pq, q→~r,r, pV (t As).

A:

Q: Find the source Q cx) Such that the So lutiim Uckit) of + Q(x) 2 ə x² 0 < x <∞ | U(x,o) = 0

A: given equation ∂u∂t=k∂2u∂x2+Qx ,       -∞&lt;x&lt;∞            ...iux,0=0 claim- find the source Qx…

Q: 2. Find the exact \ength af the following curvis

A: Arc length L=∫ab1+dxdy2dy

Q: O let T:R?→R² be a lineas tanafor- mation Such that T([:])- [ ]. T %3D Find matnie A Such that T(x)=…

A: Given that T:ℝ2→ℝ2 such thatT11=41  and T01=32 We have to find the matrix A such that Tx=Ax   ,…

Q: the following "quation sutisfied Cauchy - Rieman equation es .4 W = Z

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1.…

Q: 5. If u = ee Cos(alogr) prove that a'u 1(ôu 1 a'u = 0 + r ôr

A: Derivative.

Q: P:(A UB) cB Q :AC(A nB) Q => P I have to prove that p=>Qond that

A:

Q: State the third congruence that is needed to prove that ADEF = AQRT using the ASA Congruence…

A: To state the third congruence condition that is needed to prove that ∆DEF≅∆QRT by using ASA…

Q: Compute for the value of tanh-(1 – i) In 5 my + 2.13i In /2 + 2.13i Inv - 4.25i 2 In /2 + 2.13i

A: Let, tanh-11-i=z. Thus, solve for z:…

Q: Which theorem can be used to prove that ΔROM ΔΡΜΟ M P.

A: We can answer the question as below

Q: If z=2e(i pi/20), use De Moivre's theorem to compute z5

A: Use demoivre theorem

Q: The requved values tor a qud b tor Ple funston to be contimues at x=

A: Use simple continuity theorem.

Q: Ex 6 Show that X -Ca,i) is HOM with y- (1,00) if X and y have the euraal Seibsipace op. af R Hint:…

A: Homeomorphism: Two topological spaces and are said to be homeomorphic if there exists a function…

Q: Assume f,g : [a, b] → [c, d] where a < b and c < d. Prove that sup{f(x)+g(x) : x € [a, b]} <…

A:

Q: II. Let U = R, { x € R | 26x + 25x = 0}, J = { x €R | |4x + 2| > 10 } and K = { x € R | x? – 3x – 4…

A:

Q: Suppose that fo sf,:X-gy and g,-3 YoZ Prove that (Hint : First use ce) to show that gfe g,, and then…

A:

Q: 3. 1+x2 хр xp q Find b such that J Tuy2

A: By using integration formula we can find the value of 'b'. See attached for detailed solution.