7|32n+1 + 2n+2, Vn E Z.

Q: ds if s = Find dt 7t + 3 ds dt II

A: We have given;

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]

A:

Q: Residue of at z = -3 is (z+3)² Select one: a. -2 b. 2 C. 3 d. -1 е.

A:

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

A:

Q: If v = (x² + y² + x²) −¾7, then + O O O 1 O -1 O-1/2 Other: 8²v 8²v dx² მყ2 + 8²v əz² is

A:

Q: x2+1 =0 Has soluion in R

A: Solution:

Q: 3|n(n+ 1)(n+ 2), Vn E N

A:

Q: v.(AX 8) - 8 ·/TXA) – A (vX 8) Prove the earuation.

A:

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

A: See solution below

Q: Ifv= U (x² + y² +2²), then 025 + 0 + 02 is dy² 0 0 01 1 O-1/2 O Other:

A: Here we have to do the partial differentiation of the given function.

Q: Q1(i) Prove that 1 1 1 + 2n²+1 V2n2+2 V2n2+n]

A: To prove: lim 12n2+1+12n2+2+.........+12n2+n=12

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

A:

Q: 30. If (ai + 2j – k) × (-j+ 3k) = 5i –- 3j – k. Then %3D a = A 2 D 3 O123

A:

Q: 2. sin anod 2 -1)+2) u 2U!S o47 7.

A:

Q: Prove that L ={(1Z*)"10" | n e N}is not regular.

A: The given language: Then, the above language can be rewritten as, To prove that L is not regular.…

Q: 1)z = e(4+j3) In(6230") 2) z = (-;)(* 2) z = (-)(r)"

A: (1) The  given complex equation is                                                Z=e4+j3ln6∠30°

Q: Find L {(2t" – 3)° } . | O 4(2n)! 2n+1 12(n!) + sn+1 4(2n)! g2n+1 [ 2(n!) 8n+1 O 4(n²)! 12n! 9.…

A:

Q: 3-Evaluate S Fdr where 2X Cisgiven by rT) = C 3+U-3t)jrék

A:

Q: a) Suppose, T(n) = 1²+2²+3²+..+n2. Show that, T(n) is in O(n³). %3D .....

A: Big-⊖Notation: Let f and g be real valued functions and assume g is eventually position. We say that…

Q: 5.7.4. Show that the two formulas (r = y) and (S(r) = Š(y)) in N.

A: Hi, since there are 2 questions given, the first one is answered.  Given - The formula  x=y To prove…

Q: (9) Ifr² = x² + y² + z², then V•r is (a) 3 (b) 0 (c) r (d) None of these.

A: Follow next step

Q: -5 -71 -2 -4 -8 -3 -9 [-1 [3 -2] t A = v = |1 w = -1 and x = 1 -3 5 1 4 v in N(A)? Type "yes" or…

A:

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

A: Given: For all n∈ℤ, n2-3n+1≠2

Q: 4 Σ E Vn +1 n=-1

A:

Q: (17) Define S(n) as follows: n S(n) : i(i!) = (n+ 1)! – 1 i=1 Prove Vn e N1, S(n).

A: Consider the given expression. Sn=∑i=1nii!=n+1!-1 Now, use the mathematical indication to prove the…

Q: 5. (BH) Calculate det B, where 0. 4 1 1 В — 1 -2 4 -1 2 1 -1 0 7

A:

Q: Prove indirectly: "V n E Z, 4 ł (n² – 2)."|

A: Ans:Let us assume that 4/n2-2;∀n∈zthen we have there exist a positive integer k such…

Q: 5- 3 9-22 Evaluate the integral -3 ! VP +y*dydz. a) b)3n c)9n d)27x e)81x 10 a

A: The equation of a circle(in cartesian coordinates) centered at (h,k) and having radius r is given by…

Q: 3. Let A = {3k : k € Z} and B = {15m + 12n : m, n € Z}. Prove that A = B.

A: Let     A = {3k : k∈ℤ}    and          B = {15m+12n: m,n∈ℤ}To show :- A=B∵Let  x∈B  ⇒x = 15m1+12n1…

Q: 15. prove that L. d= nd(n)/2

A:

Q: Employ a suitable c 2n² +3n diverge (a) V5+n² n=1

A: ∑n=1∞2n2+3n5+n5limn→∞an+1an= limn→∞2(n+1)2+3(n+1)5+(n+1)52n2+3n5+n5= limn→∞…

Q: n2 for all n E N. 4n Let r, :=

A:

Q: 4. Use Cramer's rulc to solve the lincar systemn. r+ 3y 2 5.r +7y 3

A:

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

A:

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

A: We will use the standard definition.

Q: 너 ()- 3s %3D O 3te-24 O 3e-24 (1 + 2t) O 3e-24 (1 – 21) O 3e (1 + 21) O n (금) O 6te2 O 31e2

A:

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

A:

Q: 8. Prove 3n e R|n? – n < 0

A:

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

A:

Q: (2). By Contrapositive: “V n e Z, if 3| (n² + 1), then 3 ł (2n² + 1)."

A: Solution:

Q: Find the radius of convergence and interval of convergence of  Σ 1 to infinity…

A: Find the radius of convergence and interval of convergence of given infinite series.

Q: 7. E(-1)"- Vn +1 n=1

A:

Q: 2 O Expand Pn = 2x +3x +) in Term of P.f,.

A:

Q: 4 If fx> 0o ag x>a<, does fw→ 01 ven example to explan your state ment

A: Given: limx→af(x)=∞ To check: limx→af'(x)=∞ holds or not.

Q: (b) Show that V n 20 > (2i +3)3' = (n+ 1)3"+1. i=0

A: To Show- Show that ∀ n ≥ 0 ∑i=0n2i + 33i = n + 13n+1.

Q: If s(n)=3n2−3n+5s(n)=3n2−3n+5, then s(n)=2s(n−1)−s(n−2)+cs(n)=2s(n−1)−s(n−2)+c for all integers…

A: Function represents the relation between dependent variable and independent variable. Function…

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

A:

Q: 4. Prove that n(3n – 1)r x + 4x + 7x + ... + (3п - 2)x for n e N.

A:

Q: -15 ス=スーカー3;w>え崎-k md 。 d o えしデx2) ) 1パx悩)1,) (穴応)し花っ2) - %3D A. 一

A:

Q: Let f(n) = 2n – n? + 10n – 7. Show that f(n) is O(n³) using specific values of C and ng-

A: