(b) {an}, where an 1 if n is odd and an = ; if n is even. |

Q: H(x)= In(x+2)

A: our objective is to find x

Q: Which of the following is false? O ("2) = 2(") k ㅇ ") %3 (4") + (F) k n(n+1) (":"): 2 2 O ()² = (?)…

A: We have to check whether given statement is true or false.

Q: If f(x) = 5³x then f'(x) = 5.A 5h 3 In S O 3x(5³-1) 5³ (In 125) 3(5²)

A: Here, the given function is: f(x)=53x So, note that ddx(ax)=axln(a) where a is a constant.

Q: For any n e N, let An = {x € R | –n <x < n}. Prove that NneN An = A1. (Recall that we define 0 ¢ N.)

A:

Q: eferaine the radiea) of the constint e for whichiscentinuos on Eo, 00) if n<a 2n +4,if Y2

A:

Q: P is of degree 2; P(0)=4; zeros -1, 4?

A: Write the standard form of polynomial with the help of zeros.

Q: (-i)a is e(1+4n)i wheren is an integer. where n is an integer. O equal to the above O equal to the…

A: Any complex number, z can be written in the form of  z=reiθ . The complex number i can be written as…

Q: 1 If h(x) = 5 + x and k(x) = which expression is equivalent to (k h)(x)?

A: Given : h(x)=5+x   and k(x)=1x we have to find (k∘h)(x)

Q: Show in detail that E [(X-µ)^n] = 0 for ∀n , where X~N (µ, σ²) and n≥3.

A: It is an important part of statistics. It is widely used.

Q: - - 9. - [1.0001 x* H. Verify Let A 6 = the error %3D 1.0001 formula |r* – ô|| ||r|| < K(A)-

A: Let A=2112, b=33, x^=1.00011.0001, x*=11. Verify the error formula x*-x^x*≤KArb.

Q: 62. a. Show that e>1+x for x > 0.

A: We will answer the first question only as those all are different and we don't answer multiple…

Q: Show that S1 = S2 if and only if Si U S2 = S1 N S2.

A:

Q: Arg (zz) = 0, whenever :+ 0

A:

Q: - such that n >r > 1, (n – 1)! r!(n – 1 – r) n! r!(n – r)! n - r -

A:

Q: -In2 2e® cosh 0 do -In 4

A:

Q: Let a, b eR with a < b. Assume that a + <b - for all n e N. Show that n n=1

A:

Q: If x is any real number, then cosh x Σ n=0 n! + 198 Σ n=0 (-x)" n!

A:

Q: -4 -2 Let E= 0 Find 2E. -3 5

A: Given,  E=-4-204-35

Q: 12 Explain the difference between σ and σ and between μ and μz.

A: It is given that the symbol of population standard deviation and population mean. Here, need to…

Q: Show that E [(X-µ)^n]=0 for ∀n, with X~N(µ, σ²) and n≥3 being odd numbers.

A: We need to show; E[(X-μ)n]=0 for ∀n and n≥3 being odd numberswhere;X~Normal(μ,σ2) That is, we need…

Q: -2x -dx - Evaluate (1-x)' 8 А. х* + 6х- In(1-х)' + 1-х 8 -(1-x)* +C С. х? +6х+ In(1-х)' +- -(1–x)*…

A:

Q: For which positive numbers a is it true that ax >= 1+x for all x?

A:

Q: -a = Y express L and K as expressions of

A:

Q: -10 If AXT = B, then X= Let A = %3D 0 2

A:

Q: What is/are X-value(s) in ex2-3x+2)= 1? 1 (2,1) none of these O O

A:

Q: In SOR method the value of 0 < w <1 Select one: True O False

A: We will use the formulation of SOR              (Successive over Relaxation) Method to     show what…

Q: Then k is equal to

A: We know that integration of density function over whole range of x, is always 1. We will use this…

Q: Let n be a positive integer, then n+1≥ for all n.T/F

A: We need to show that n+1≥n for all n where n is a positive integer. Lets proof by contradiction

Q: leoinov o and 7o iqeng od dw nislqont-( do (0) d o on tud pouso mbrore XE G Such that X? -3X -4=03…

A:

Q: e3x + 6 enx e(n+1)x = 1+ e® + 2 Sx n! (n+ 1)!

A: The given series is : eex=1+ex+e2x2+e3x6+·····+enxn!+en+1xn+1!   Let fx=ex The above function can be…

Q: - is a real num 1S y+z= 6, 4x +

A:

Q: Q: Prove that : sin' ne -de = na for all n e N. sin' e

A: solution is given below

Q: 2. Show that coo(N) co(N) § c(N) Ę e^(N).

A: To prove that c00N⊂c0N⊂cN⊂l∞N. By definition, c00=x∈lp|all but finitely many xj's are zeroc=x∈l∞|xj…

Q: ( Σα - xi-1) = x = x for n > 2. i=2 11 IDDLE: following "proof" th

A: Given that c, x1, x2, ..., xn, y1, y2, ..., yn are 2n+1 given numbers.

Q: (9 sin z = @ True O False

A: given, sinz=0

Q: 1 x? + k by considering several cases for the constant k.

A: Let k be equal to a2. k=a2a=k Use the formula ∫1a2+x2=1atan-1xa ∫1a2+x2=1atan-1xa∫1k+x2=1ktan-1xk

Q: 1 The x value(s) if 2**z = 128*

A: We have to find the value of x for the given equation: 2x+12=128x We have…

Q: O None of these Oe equal to the above Vdows O is equal to the above O is equal to the above 434

A:

Q: Find all values of x for which ∑ (n=0 to ∞) 1/(1+x)^n equals 4

A:

Q: expressed

A:

Q: Let b₁ 2 = sin−¹ (²) and c, = sin-¹ („²7) for all n € N such that n ≥ 2 +00 Σ(1+bn) n=2 Σ(bn-Cn) n=2…

A:

Q: 5 + 2 sin(n?) n=1 n2 (b) Σ Vn5 + 100n² +1 n=1 In n (c) E(-1)*+1; n4 n=1

A:

Q: 3s +8 14. If F (57 キind f(t) キ12s +52

A:

Q: 2. (a) Evaluate e²-dr, where a > 0.

A: Let, I=∫0∞e-x2-a2x2dxI=∫0∞e-x2e-a2x2dx Let F(x,a)=e-x2-a2x2DaF=-2ax2e-x2-a2x2DxF=-2x+2a2x3e-x2-a2x2

Q: 8. Prove 3n e R|n? – n < 0

A:

Q: If a test is run and p = 0.0356, then we can reject H0 at  = 0.01.  True  False

A: The given level of significance is, α=0.01 The p-value of the hypothesis test is, 0.0356

Q: Q4/ If A = 3 - l: prove A-A-5I = 0

A: Given that: A=213-1

Q: If var(e) → 0 as n → 0, then 8 is said to be

A:

Q: (-1) is where n is an integer. equal to the above e(1+2n)i where n is an integer. equal to the abov…

A: We know from eular formula e^iθ = cos θ + isin θ

Q: ? Suppose that * f(3) = }, and f(x) > 0, and f(x) < 0. Is it possible that Í(2) = . 3 O False True

A: