28 + 58 lim z-5i z7 – 54iz3

Q: 1 a) lim n+00 V 0. 8 ) lim b) noo n+3 0. 5n2 – 3 (c) lim n0o 9n2 +4

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Q: )"-( 18 6. lim V n4n +(4n)" 2+ n2 4 4+ n2

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Q: In2 + 5n + 4 lim an = 1 %3D %3D 3n2 + 8n + 8 n-00 1n? In2 5n + 4

A:

Q: 6. lim t+0o e3t + 4t

A: Given: limt→∞t2e3t+4t To determine: The value of the given limit.

Q: Show that 1 Σ (z – n)2 cosec² (z) 8.

A: As we all know the theorem which states that, For z∈ℂ\ πℤ 1sinz=∑n=-∞∞-1nz-nπ=1z+2z∑n=1∞-1nz2-n2π2…

Q: 6+2f(z) If 12e|< 3, then lim, 2f(z) = %3D 4-27 Select one: O 3 O -1 0 1 O 2 O None O-3 O-2 O- 1

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Q: Prove that x4+4=(x+1+i)(x+1-i)(x-1-i)

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Q: [0 1 If A= find x and y such that (xI +yA) = -1 0

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Q: Q5: Define nilpotent element. Are 1 and 3 nilpotent elements of Z9?

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Q: 4n+1 b] lim %3D n+3

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Q: 8. 7.6 - (-10.1) = 2. %3D q. 15.7 - (-9.6) = %3D SUBTRACTING FRACT UNLIKE DENOMIN -3-(-) %3D Aug 19,…

A: 7) -8.8 - 3.4 = - (8.8 + 3.4) = -12.2

Q: Let bn : n° +n+6 for all n ɛ N. Find limn→∞ bn- 5n3+4

A: Given that bn=n3+n+65n3+4 and we are required to calculate limn→∞bn. Therefore, we are supposed to…

Q: Prove that 1 1 1 Lim Jan+1 + V2n²+n. /2n²+1 V2n²+2

A: Limit is defined as the value of the function , when number of terms tends to infinity.  It can be…

Q: (Зп+5 Find infimum of A |n E N} n+9

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Q: -In2 2e® cosh 0 do -In 4

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Q: (2) Find all the numbers z such that elz = 10i.

A: Consider the given. eiz=10i

Q: NEED ASAP PLS!! Use exact values whenever possible! 1. 3z^2-(5-j4)z+(2-j3)=0

A: The given equation is: 3z2-5-j4z+2-j3=0 We have to solve this equation for z. Required formula:…

Q: 11. Evaluate the integral. +3 x² + 4

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Q: nd to wnwyun g ans 2

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Q: Use Heaviside Expansion Theorem (2s^2+1)/[(s-2)(s^2-2s+5)^2]

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Q: 9n – 5 a) lim n-- 3-n - 18 1 2n2 + 3n – 5 8n? +1 1 b) lim n- o0 || 4

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Q: Prove that 2n3 + 5n 1 n? (i) lim n→∞ 4n³ + n² (іi) lim 1. (п — 7)2 — 6 2 n-00 ||

A: Let us consider, f(n) = (2n^3 + 5n)/(4n^3 + n^2) Dividing the numerator and denominator by n^2 we…

Q: In(2z + 1) lim O 00 01 0 2 00

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Q: 3.2 Find and classify zeros of z³(e² – 1).

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Q: lim/ 63-64 t*-7t+12 い+ E-4 6²- 34 -4 j + 3(t-y) In(t-4)£ ニ

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Q: If x1=2, Xn=4X(n=1)–4n Vn22. Find the general term xn

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Q: |2а — 10| limr→0- -1 x-5 O True False

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Q: 1. Find an r> 0 such that all zeroes of 24 + 6z²+z+3 are contained in D,(0).

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Q: Show that 100 1 arctan(100) – arctan(2) + 1 Σ 1+ k2 k=2 < arctan(100) - arctan(2) + 1+ 22 1+ 1002

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Q: 4. Let z = -4 + 3i and zw = -7 - 2i. By showing clear steps, find w in the form of | | a+bi.

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Q: cos(n") In(4) 1. 1 2. n In(n) n%3D 6n + 3 (-1)" n=1 1 4. n - 5 3.

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Q: 2. [xy z] ム 2 2 6. Prove ît 4 3

A: matrix multiplication

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

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Q: In n こ0 lime 2) lim Yn 3) lin メー

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 2. Prove 1+5+9+13+ .…+ (4n – 3) = n(2n – 1) using PMI. ... %3D

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Q: 1 find func- 88. Finding a Composition If T(x) = %3D Vi + Vx tions f. g, andh such that fo goh = T.

A: Given: T(x)=11+x To find f, g, and h such that f∘g∘h=T

Q: 5. Find the v alue of x. 5x – 4 x + 6

A: Given :    To determine : The value of x.

Q: z/(z-3)2 dz ; C: |z+3| =3 slove by residue theorem

A: The given integral is,

Q: 8. Determine whether v(x) = r'+3|x| even, odd or neither. Discuss its symmetry.

A: Q8) Given: v(x)=x3+3x

Q: 1. Find z for x = 4.7 %3D 2. Find x if z = 3.2

A: Given  Sample is normally distributed with mean 5 and standard deviation 3.8

Q: 2. (a) Evaluate 7n+1 +2" i. lim N; n-00 7" – 2n | ii. lim Vn2 + 3n – Vn2 – 3n |, n € N, n > 3. n-00

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Q: 00 (1) 2n 27. n=1 А. 2 В. -3 С. D. Е. Divergent

A: (27). The sequence is defined by To determine : The value to which the sequence converges.

Q: 17. Prove thatsin x = =x 1-x2 dx

A:

Q: x+1 Q1/ Prove that coth-1 x = 2 x-1

A: In this question we need to show coth-1x=12lnx+1x-1.

Q: 2) × 2+4i 3+1 and 2=3-1 2+i 2 prove that x² + 3xy + y² = 6 if it was

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Q: 2+4+... +n lim 7n2 + yn

A: limn→∞2+4+....+n7n2+n

Q: 5n+7 Find supremum of A :|n E N 4n+12

A: Given set isℝ A = 5n+74n+12 | n∈ℕ We know that a number u is the supremum of a nonempty subset S of…

Q: 7- x"(t) – 2x'(t) = 6 – 4t x(0) = 2 , x'(0) = 0 nat

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Q: x+1 Q1/ Prove that coth-1x = x-

A: