n° Prove that =n² + o(n). n² – 1

Q: Equating the coefficients of corresponding powers of t gives 2/3(13A2 + 2) = 10A2 + 1, (2.200)…

A: 2313A2+2=10A2+1   .....(1)2935A3+10A2=10A3+2A2     ...(2) We need to solve the equations to find the…

Q: Q5/ Show that the following IVP has a unique solution and find the exact solution: 2 y'(t) = y +…

A: Answer

Q: 19. Let a, = (-1)" Vn 2 1. Calculate the value of an+1 - a, for odd values of n. %3D А. -1 В. -2 С.…

A: As this is a multiple question type, according to Bartleby Answer Rule, only 1st question is to be…

Q: Q1: Prové by induction nzZ! ☆ (1- 1 htI ( Here JJ (Pi") stande for froduct) means (I- I

A: A detailed solution is given below.

Q: x+2 Q2) k(x) -Vx – 2 , n(a) = x²(x² + 1)¬1, mx) %3D 3-x Find a formula for (n oko m).

A: A composite function is a function that depends on another function. A composite function is created…

Q: Z1 is complementary to ZM 22 is complementary to ZM Z1 = 2 Given: Prove: M R 2

A: Given: ∠1 is complimentary to ∠M. ∠2 is complimentary to ∠M. To prove: ∠1≅∠2 According to the…

Q: d a value of r> 0 such that h(z) = z² +22³ + z + 1 has all its zeroes in D,(0).

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Q: n Find the general solution of o ( :) (2)*y(n-i) =0. ata of any nonzero real

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Q: Q3:B. Find the convolution between the signals h[n] and x[n] shown in Figure below using analytical…

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Q: 3) FIND A PARTICULAR SOLUTION OF THE ODE y"+8y-20y = 2x +5 - e?X %3D

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Q: (a) Find the real constants P,Q, R, for which 3 P Qx + R x2 - x + 1' x3 + 1 x + 1 Show that V3 dx =…

A: Show that: ∫013x3+1dx=ln2+π33 Used formulas, ∫1x+adx=lnx+a∫1x2+a2dx=tan-1x

Q: z3+4z+9 Residue of f (z) at z = -1 is %3D (2z+2)(z-3)³ a. -1 64 O b. 1 64 O c. -1 32 O d. -1 16

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Q: /2r-z2 Evaluate: Jo J dydr O- 3 O 1 1/2

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Q: The solution of e² = -2 for n = 0,±1,±2,. is %3D ... Select one: O a. In2 + in(1+n) O b. In2 +…

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Q: O Express the following functrons in the form u+iv •f(2)%3In (I+z)

A: Given function f(z) = ln(1+z), z=x + iy. We have to express f(z) in the form u+iv, where u is the…

Q: 4n +5 Describe the long run behavior of f(n) = 3nº – 5n° As n → – 00, f(n) → As n → 00, f(n) → Add…

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Q: (a) Find the least positive k E N such that 3* =10 1. (b) Using this k, prove: for all m e N, 3m =10…

A: (a) find the least positive k∈ℕ such that 3k≡10 1 b) using this k prove that : for all m∈ℕ 3m≡103m÷k…

Q: Find n if P(n+14,2) = 756. Show your steps using the formula for P(n,r). LIca tho aditor to fo

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Q: (a) Find all the solutions of e²+e¬z cosh z 4. (Hint: cosh z -) 2

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Q: 3t Q3) Verify that -e-3t e 3t are solution for re-3t 3t 1 e-3t -2 21 2 X on (-0, ∞). 2 X': -2 1 2 1

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Q: How do I calculate this? If Z~N(0,1), calculate Pr(1.55 < Z < 2.65)

A: Given that, Z~N(0,1)

Q: If x1 = 2, xn = 3xm-1 + 2, Vn > 2. Find the general tem æn

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Q: d. The distance a freely falling body covers in the nth second is given by S(n)=d(n)-d(n-1). Show…

A: We know distance traveled by a freezing falling body in n seconds is given by  dn = 1/2(gn2)

Q: E-o(-1)"(n+ 1) x“ = (1+x)² 1 2.b) for |x| < 1 %3D n=0

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Q: ´n +i n+r +1 Prove that : k i=0 k +1 k+1)

A: Binomial series

Q: Show that g(t) = t2tant takes on the value ½ for some t in [ 0 , π/4 ].

A: gt=t2tant on the interval 0, π4. When t=0, g0=02tan0=0 When t=π4, gπ4=π42tanπ4=π2161=π216=0.6168

Q: x' + 2e* – In xr- 3 = 0

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Q: Find length of the cardioid r=a0³from 0 = 0 to 0 = n %3D

A: Length of the cadioid is given by below formulaLength = ∫0πaθ3dθ

Q: Proof: böt: if m #n 1-iħ if m= n 0, m or n = x,y,Z Pm Pn] : %3D

A: Given that, pm,n=0m≠n-ihm=n The objective is to show that, Pm,Pn=0. If m is not equal to k and n is…

Q: (z- 1) The residue of f(2) = at z = -9 is -9e9 (z + 9) Select one: O True False

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Q: (3) = 2 u + U, =D2 at ucx, t) fipdy ing the following initial condition : - -3X U(x,0) = 6e

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Q: (c) Derive the following formulae (i) Σ Fra"(n+1) 2 (ii) n(n + 1) (2n + 1) 6. r=1 (ii) 2 n(n+1 2 r-1

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Q: 27 Find (all) the value(s) of c such that 3c2n 8. %3D n=0 (A) c=3 (B) с 3 4 (C) c=-33 (D) c = } (E)…

A: Substitute the value of c as 0, 1 and 2 in the nth term to find the generated series.

Q: 82 (1+) V3 – i By using De Moivre's theorem, solve:Z =

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Q: -2) Calculate A-1 by 2 Let A = 1 2 1 -1 -1 A-' = ÷(-A² + 3A +I). and verify your result by showing…

A: Given: A=12-2121-1-10 Therefore,…

Q: Find the value of k so that the value of S,"(2y – 1) dy is 10. 1 2 3 4

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Q: =Xtanx dk, Prove that ="IH (n+1)I,+(n-1) -1 T 1 2 n

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Q: R(Z) = 22212 S2)ク りェ Find. (ROR)( (Sos) (2)

A: Given function                                                 Rz=2z2+2 and Sz=3z…

Q: 2km+3(m+k)+4 E(Xkym) = (k+1)(k+2)(m+1)(m+2) where k and m are both nonnegative constants. Determine…

A: Given Using the joint distribution describing X and Y, the following formula was derived   where k…

Q: 4- Find e' in the form x+iy if z equals a) 2+ 1/2n i b) 0.5 -1.2i

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Q: 27 Find (all) the value(s) of c such that 3c2n 8. n=0 (A) c= 3 (В) с— 4 (C) e = -} | (D) c = } (E) c…

A: Given, To find the value of c. The formula for the sum of an infinite geometric series is, where a…

Q: Do Residues Add Up? (z+1)(z+6)(z+10) z(z+2)(z+3) 1. What is the residue of at z = 0? (z+3)(z–2)²…

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Q: nex}. 2n (b) Let B = 3n +1 i. Prove that inf B= ii. Show sup B

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Q: Q3/ For the signals in the figure find the convolution using direct formula * 3.0 2.5 2.0 4. 1.5 1.0…

A: The table is given below: k 0 1 2 3 4 x(k) 1 0 2 3 3 h(k) 4 2 5 6 3

Q: rcise : The residue at z = 0 of f(z)= (2-2)(z-3)(z-5)™. (a) 0 (b) -10 (c) 10 (d) none of these

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Q: 3 (a) Given that T= 2n12g , express I in terms of T, g and n. %3D

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