2. What is the quotient of and?

Q: Show that if a|b then -a|b.

A:

Q: Show that for baetween ( tana

A: Show that for x between π4,1 for the function tanxx=32.

Q: Let X and Y be independent, and let X be N(10, 1) and Y be N(11, 1). PIX >Y),

A: From the given information, X and Y are independent random variables. Let X be a N(10, 1) variable…

Q: 1) Evaluate whether y, and y, are uncorrelated 2) Evaluate whether y, and y, are independent

A: Given, y1y2 = 111-1x1x2 So,  y1 = x1+x2y2 = x1-x2 And, Mean is 0 and Variance is 1 So, E(xi) =0…

Q: Derive u and show that 7 X is biased estimator of 2. Can you modify 7T -X in order to get an…

A: The expected value of X is defined as  μ=∫λ∞x.f(x)dx And an estimator to be unbiased its expected…

Q: Let a, b, x, y ∈Zbe such that ax+by= 11. May we conclude that gcd(a, b) = 11?Why or why not? (Write…

A: Consider the given information:Let a,b,x,y∈ℤ be such that ax+ by=11.

Q: What is the domain of h- (x) ifh (x) = x2 ? %3D O (00, 0] O (-00, 00) O (-2, 2) O [0, 00)

A:

Q: 3 2 If A = use the Cayley-Hamilton theorem to determine A?. 5 1

A: We can solve this by using given information

Q: Suppose is dhe iavene faction of a diffarentiable šunc- tica fand let Glu) -1/r . E3) - 2 and /3) -…

A: G(x)=1f-1(x)f(3)=2 , f'(3)=1/9

Q: 3. Find and and y= ivative of

A:

Q: Let ā = and b . Find 3ā + b. -

A: We will simply use vector addition rules to find the answer

Q: Let, a, = 3, a2 = 4 and for n2 3, a,= 2an-1+ an-2 + n + 1, express a, in terms of n. %3D %3D %3D

A: The nth term of A.P is given by an=a+n-1d we have,  a=3,d=4-3=1an=3+n-11=2+n we get,…

Q: but not こ *6A-エ none of thesce

A: Let us assume two matrices A and B. To prove or disprove if AB=I then BA=I. Let us consider matrices…

Q: Given and prove

A: Given,

Q: & 18) Vaing show that the idntity (i+a5^= (1+x)" (1+x), 2

A: The given problem is to prove combinatorial proof using basic binomial identites, we have to show…

Q: 3 10. Show that R² span

A:

Q: (b). lim zInz² et

A: To evaluate: limx→0 xlnx2ex Using logarithmic property we can write the given limit as  limx→0…

Q: so-Z of what is 21

A:

Q: Let, a, = 3, a2= 4 and for n2 3, a,= 2an-1+ an-2, express a, in terms of n. %3D

A: we have the nth term of A.P is given by  an=a+n-1d here,  a=3, d=4-3=1an=3+n-11=2+n we get,…

Q: 4. Prove that C, = ,C4 (Hint: Algebraically show that the Left Side = Right Side)

A: We know that  Cr n= Crn = Crn = (n)!(r)! × (n-r)!

Q: 3. Is this sentence consistent? “There is someone who loves exactly those people who do not love…

A:

Q: If A =I then what is A'?

A:

Q: Which of the following things is NOT contained in B? R

A: Given that the plane B, here we have to find the things is not contained in B.

Q: Use the given information to prove that ADEF ADGF.

A: We need to find out the reason and complete the proof .

Q: Prove that R(5, 5) < 50.

A:

Q: Prove the following. 2. If alc and a+ b = c, then alb.

A:

Q: 3. Let r and y be positive integers. 4. Let a, b, c e Z. If c divides a +b,

A:

Q: Describe the elements in Q(π).

A:

Q: how me t

A: Given, equation  (4), we have    wn+1=∑p=01wn-p∑h=12zn-hzn-ε+μ    and zn+1=∑p=12wn-p∑h=01zn-hwn-μ+ε…

Q: . Given: LAOM and LMOC are supplementary. Prove: x = 50

A: To prove that x=50

Q: Construct a paragraph proof to prove the following: Given: y +2 = (x- 10) Prove: y =x-8

A:

Q: 4. Prove or provide a counter example for the following: (AU B)nC = (AnC)U(BnC)

A: We need to prove that(A∪B)∩C=(A∩C)∪(B∩C)If we have to prove that(AUB)∩ C C C…

Q: Are there numbers a and b such that |a + b| &gt; |a|+|b|?

A:

Q: 4 Write the allIV Algebraic Identities with complete explanation.

A:

Q: ,- ). Show that there a 3,4

A:

Q: Describe the elements in Q().

A:

Q: have the following properties:

A:

Q: 20. (gof)(x) and it's domain.

A: Topic = Functions

Q: Examplen' find the pvoduct of the follow ing (wo natricesi 2. 2. ら 1. 又3 3.

A:

Q: 11) Suppose an>0. Which of the followill

A: This is a question from the series.

Q: 21, Referring to Example 50.9, show that G(Q&2, i/3)/Q(i 3) ~ (Za, +).

A:

Q: 21pi/11 is coterminal with ?

A:

Q: Consic and b whose divisic demor exist r

A: let R=ℤ-2 function is defined as da+bx=a2+b2 and dxy=dxdy now, for x,y∈ℤ-2  xy-1∈ℚ-2 then, for s,t∈ℚ…

Q: How many extensions of g to A are one-to-one? How manu ou

A:

Q: 22. Use the adjoint of 1 -5 -1 A = 0. -2 1 to find A-

A:

Q: Suppose x ~ Uniform(1, 2), and

A:

Q: (c) If gcd(a , 133) = gcd(b , 133) = 1, show that 133|al8 b18 %3D %3D

A: