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

Q: 4.) Find the value(s) of k such that A is singular. 1 k 2 A = -2 -k 3 1 -4

A: The given matrix is                               A=  1  k    2-2  0 -k   3  1 -4 We have to find…

Q: If TeZx Such that x is a momber of 27+5x-3=03 and S={x Such that x i. member of 2i+71+233/3 that T…

A:

Q: If the function (x) =sin 2(2n+1)x for some positive integer number n, then the conclusion of Rolle's…

A: Given that: f(x)=sin2(2n+1)x on the interval π8, 3π8.and satisfies the Rolle's theorem at…

Q: 4. y=e2 y=e", x= In 2, and x = In 8 %3D

A:

Q: ii. Show that the image of the hyp n2 = cos2n

A: Introduction: Inversion and Reflection: The transformation is w=1z.

Q: 2. M is at -2 and N is at 14. Find the point X so that X partitions M to N in a 3:1 ratio.

A:

Q: 15 Using intermediate value theorem, the equation x² + = 4x has a solution over O 1,21 O 10,1[ 13,4[…

A:

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

A:

Q: 1. Using (2n +1)Pn= Pn+1-P-1: prove that P(x) = (2n-1) Pn-1(x) + (2n-5) Pn-2+(2n-9) Pn-3+.... - and…

A: Given : 2n+1Pn=Pn+1'-Pn-1' To Prove : (a) Pn'x=2n-1Pn-1x+2n-5Pn-2+2n-9Pn-3+ . . . . . .…

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: Applying the Cauchy's Residue Theorem, evaluate de (5 – 3 sin 0)²

A:

Q: A cubic spline S is defined by: if 25x53 if 3 5x54 So(x) = 3(x – 2) + (x – 2)² – 4(x – 2) S(x) 5,(2)…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: х Prove that 1 < < sin x for all x e (0,5). - ド|N

A:

Q: 1 Expand in ascending powers of x, up to and including the term in x', simplifying the V(1 –2x)…

A: To solve the following problem

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

A:

Q: 4. Using Z(n)= Show that Z(ncos no) = (z-1) (z'+2)cos0-2z (2-2zcos0+1)

A:

Q: 3V Show that there dã do not exist two real numnbers which add to 7 and multiply to 13. It is not…

A: our objective is to conclude the result

Q: nd to wnwyun g ans 2

A:

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

A:

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: A cubic spline S is defined by: So(x) = 3(x – 1) + 2(x – 1)² – (x – 1)³ if 1< x< 2 S(x) = 1 s, (x) =…

A: Given,Sx=S0x=3x-1+2x-12-x-13                             if 1≤x≤2S1x=4+4x-2-x-22+13x-23…

Q: 12. Start with the identities x2 1 P, (x) = xPn-1(x) + *P(x) n P, (x) = xP-1(x) + nP,-1(x ) (a) Show…

A:

Q: (z+1)(z+6)(z+10) z(z+2)(z+3) 3. What is the residue of at z = -2 (z+3)(z–2)² (z+2)(z+6) 4. What is…

A: 3) Given f(z) = (z+1)(z+6)(z+10)z(z+2)(z+3) Then Res(z=-2) = limz→-2(z-(-2))f(z)= limz→-2(z+2)f(z)=…

Q: (a) A rectangle has area of 96 ft2 and perimeter of 40 ft. Find its dimensions. (b) Prove the…

A: 5.  (a) Given that the area of the rectangle is 96 ft2 and the perimeter is 40 ft. Let x be the…

Q: 9. (a) Prove that v10 is irrational. (b) Use part (a) to prove that v2 + V5 is irrational.

A: To prove the given statements.

Q: 2.2. Given: y and xo = -x < ¤1 < x2 < ... < æn < xn+1 = x, where n = 256. Find the minimal number of…

A: According to the given information it is required to find the minimum number of steps to find ‘I’…

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

A:

Q: Show that r n2n-1 r=0

A: Want to  prove:    ∑r=0n rnr=n2n-1

Q: iii) a) Prove that Pa(-x) (-1)".Pn(x) u (2n)! 22 (n!) b) Prove that P2n(0) = (-1)".- %3D

A: To prove- Pn(-x)=(-1)n.Pn(x)P2n(o)=(-1)n.(2n)!22n(n!)2

Q: lim (7,y) (0,0) (4+ (2² + y²) In(x² + y?)) O 00 O does not exist O -0 O 1

A: Recall: Limit of two variables : Let f be a function of two variables .The limit of f(x,y) as (x,y)…

Q: () 2k = 3", Vn E N k k=0 k n+1 Σ 2 Vn E N, n > 1 3 k=2 į * () 主) n 3k = 4", Vn E N %3D k k=0 = 2"-1,…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1. Prove that fraction where m is z-4

A: Given: zn-1z-1 ⇒zn-1nz-1 ----(1) Let apply the limit in equation (1) limz→1zn-1nz-1 ----(2) Let n=pq…

Q: p(x) = (e³x+5 + n)³. q(x) = In(5e* + 6 tan x). u(x) = e*In(x)-x+2.

A:

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: The characteristic of Zs[x]/ is 6. O None of the choices

A:

Q: The base of a three-dimensional figure is bound by the line y = x + 4 on the interval [-3, 1].…

A:

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

A: The given integral is,

Q: (a)Show that,if x is small enough for its cube and higher powers to be 1 neglected, = 1-x +. by…

A: It is given that x is small enough for its cube and higher powers to be neglected. It is required to…

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

A:

Q: The kth harmonic number is defined to be Hk = 1 + 1 2 + 1 3 + · · · + 1 k . Prove that for all n ∈ N…

A:

Q: The characteristic of Zs[x]/ is 6. 3 O None of the choices

A: The characteristics of the function

Q: 1. For positive integers i, j,n such that i+ j = n (a) show that corresponding multinomial…

A: sol(a) we know that multinomial co-efficient is definedby ni,j=n!i!,j!  —(1) where i+j=nnow…

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: If  y = tan-1( k x) + tanh-1( k x)  and  (1 - 256 x4 ) = A Then A +k =..........

A:

Q: 14. Substituting appropriate values for x and y into the formula of Theorem 9, show that (a) = 2";…

A:

Q: Simplification of In x + In(x + 1) = 0 is x² + x – 1 = 0; x > 0 O x² + x +1 = 0; x > 0 O x? + x-e =…

A:

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.