1. For an = 5n2 + 9n3 + 1, an = n2, prove or disprove: rn = O(an) (n → o)?

Q: Let S, := (1 - (-1)"/n :n e N). Find inf S, and sup S,.

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Q: What is eh REF of B? 1 2 1 1 B = نه who 1 0 -1 به T NC vсы N 5 0 2]

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Q: 3n³ + 20n² + 5 is O(n³)

A: Given: The given expression is 3n3+20n2+5 is 0(n3),

Q: The solution of y = eY 2* , y(0) = In(In(2)) is y= In(In(2)) - In(2 -2*). Select one: O True O False

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Q: If I, = S e cos" xdx, where n > 2, prove that In 1+n(n-1)In-2 n² +1

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Q: dn-1 for all n E Z with n > 2. Prove that for a 2. Let d = 2, and d, neN, d, =. %3D %3D %3D

A: Mathematical Induction is a special way of proving things. It has only 3 steps: Step 1: Show it is…

Q: The solution of the IvP Elb+2)jl&+2)y=t", yL3)=o exists in the interval O 6, 00). noncof the giren…

A: given differential equation is t(t+2)y'+(t+2)y=t2,y(-3)=0

Q: Consider a, = V4n² + 3n – 2n for n > 1. %3D -

A: Introduction: The sequence is a set of functions with the set of natural numbers as the domain of…

Q: 4 The value of 2 n=1 3n2 will be + 6n .... .

A: See solution below

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: Given the DE as 2xy² + 4 = 2(3-x²y)y'. A. prove or disprove if the given D.E. is exact. B. If it is…

A: The given differential equation 2xy2+4=23-x2yy' Exact differential equation:    The differential…

Q: 5. Use Taylor's theorem to write down an explicit formula for R, (1). Conclude that R, (1) + 0, and…

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Q: 2etūsw ER' such that and iov-2.Than (3ü)(B)

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Q: If (ax+bx) = and k-1 n+1 8. E = 4 , then ar (ar-br) - k-1 n+2 k-1 O None 2 1/2

A: •  using elimination • find limit for n =infinity

Q: If (ar + br) = 2n %3! n+1 and k-1 8. E(ak - br) = n+2 - , then ar %3D k-1 k-1

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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: 4. Work either (a) or (b), NOT BOTH (a) Let In = for n E N. Prove that nIn = 0. 0, n n%=D1

A: a. Given that    In=0,1n  for  n∈ℕ. And we have to prove that…

Q: Σ n=1 5n Vn3 +1

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Q: 5) Show that n(n+1)(4n-1) E"=1 r(2r – 1) 6 Hence find E015 r(2r – 1) |

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Q: 8a, 2+ 225n for n> 2 with initial conditions ao 7, a1 83 %3D

A: Given: an=-6an-1-8an-2+225n for n≥2 with initial condition a0=7, a1=83. To find: The solution of the…

Q: D. Show that if an 3n3 - 17n2 + 2n - 6, then a, = O(n³).

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Q: For positive integers n and k (k sn+ 1), the kth term of (a + b)n is given by

A: The binomial expansion of (a+b)^n is

Q: Show that for all n e Z, n? – 3n +17 2. -

A: Given: For all n∈ℤ, n2-3n+1≠2

Q: Evaluate In r dydx y – K + 13

A: In this question we have to find double integral.

Q: Show that the following DE are Bernouli type and solve: 1. y’ – x = y 2. s’+ 2s/t = s 3 t 4

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Q: If E (ar + br) 2n and n+1 k=1 Σ (ακ-bk) -- 1, then Σa- n+2 k=1 k-1 O 2 3 2 O 1 5. 2 Ο None

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Q: In the process of calculating L − 1 {3s + 4/s2−6s + 205} an equivalent expression is obtained given…

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Q: 34) Ź (K²_2K) is e (n3) Ź ķ? ビ=3 Ź 2K = k=3 ntro)(2n+1), entntt) Sungs are さ。 2n3+ 3n?+n – ant- Gn…

A: We have solve the given  problem

Q: Z1 is complementary to 2; 2 is complementary Given: 2 B 3 A E to 23 Prove: BD || AE

A: Prove that BD∥AE.

Q: FOR N=195, by fermat's theorem an-2 =

A: Given: FOR N=195, by Fermat's theorem an-2

Q: 3. If X' such that the second solution is of the form X, = te+Be, then B = Select one: O a. Ob.

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Q: Evaluate plti 5. S z² dz using the formula [2² dz = A 3

A: This question is related to definite integration, we will solve it using given information.

Q: If (ar + bx) = 4n and n+1 k-1 (ak-br) = then ar = n+2 k=1 k-1

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Q: = o sdue the second solution of the Qifferentiol equotion with the help of Abel formula yu-27y'+d'y=

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Q: 6. Which of the followg quti dy (a) de dy (b) de () +2ry- (e) (4) Al of the above

A: It is given that There are four differential equations option.

Q: Ques tion 1 : that Given 2 x?y" + x y' + 3y= 0 show 2x* ylara) lanni)x ylurs) + (2n2.n +3) ym)-

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Q: es lls ew zeiflucifiib ons einiseen stigesber Show that for neN, (2n)! ' (r!)² ((n −r)!)² - 7=0 2n -…

A: We will use binomial expansion to prove given relation

Q: For xn = 5n² + 9n³ + 1, an = en = n², prove or disprove: an = O(an) (n → 0)?

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Q: 4|5" – 1, Vn e N

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

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

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Q: The solution of y' = eV 2* , y(0) = In(In(2)) is y= In(In(2)) – In(2 – 2*). Select one: O True O…

A: Proceed as shown below

Q: In Euler's method, wk = y(tx) for k = 1, ..,n. Select one: O True O False

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Q: 1),Given: AB || CD; AC 1CD Find: x and y A, ax ay by 4,

A: Here given as Given  CD||AB Also given ∠ACD=90Then∠CAB=909x=90⇒x=10

Q: For n EN, Dn = n! n k=0 (-1)k k! Thus, Dn n!

A: Explanation of the answer is as follows

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: Let c, = M and Cn = 2cn-1 - 1 for Vn eZ+ - {1}, find the explicit formula for the nth term for n…

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Q: (3b) Let n E Z. Prove that if 3|(2n² + 1), then 3 ł n

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Q: Show that yn Z, if n³+5 is odd then n is even

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Q: In Euler's method, wr = y(tx) for k=1, · .., n. Select one: O True O False

A: if you find my answer helpful please put thumbs up. thank you. the required solution is given below…