Let x be a real number such that 3 n=1 diverges. Which of the following could be the value of x? Select all that apply. O -4 || O-3 0 -2 0 -1 0 1 0 2 O 3

Q: 00 17. Let S = . Verify that for n > 1, n+ yn n+ Jn n+ yn Can either inequality be used to show that…

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A: As Per our guidelines we are supposed to answer only one question.

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Q: Which of the following statements involving sigma notation is always true? η η η Α) E (ak bR) = E…

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Q: Let T(N) = 1. T(floor (N/3)) + 1 and 7(1) = T(2) Prove by induction that T(N) ≤ log N + 1 for all N…

A: Given: TN=TfloorN3+1 T1=T2=1   To Prove: TN≤log3N+1 for all N≥1, using induction.

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A: given isA=1054-1065kmatrix A is singular if |A|=01054-1065k=01(-k-0)-(4k-0)+5(20+6)=0

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A: We need to prove that there is no positive number M such that each natural number n,

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Q: 3. Let G = Q3. Find the right cosets of H in G for: a) H = ( K). b) H = (-1).

A: Let G=Q8. We need to find the right cosets of &lt;K&gt; and &lt;-1&gt;.

Q: Prove the statement below. Let A = {x | x = 4k for some k E Z} Let B = {x | a = 2k for some k E Z}…

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Q: 1. Let, a1 = 7 and for n 2, an An-1 express an in terms ofn. %3D ". **

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Q: One of the following divergent 8. 2n

A: let us take option number d)  ∑n=1∞an=∑n=1∞(-1)n2n2+12+3n2⇒an=(-1)n2n2+12+3n2

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A: Given that                     A=x| x=4k-1 for some k∈ℤB=x| x=4k+3 for some k∈ℤ

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Q: (8) Find the infimum, minimum, maximum and supremum of each of the following sets (write d.n.e. if…

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Q: Suppose I is an open interval and f € C°(I). Show by induction that ffor х, а € 1, f(x) = f(a) +…

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Q: +1 X What are all of the values of x ,such that (-1) n+ converges? 6 06.2 O 0<x<6.3O x26.4O

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Q: Consider the function g(x) = x - 6x + 5. Which of these intervals must contain a solution to g(x) =…

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Q: (2) Let f(x) = ax³ + bx? + cr + d, where a, b, c, d e R and a + 0. Prove that f(x) must have a root.…

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Q: Suppose f(z) = In z and g(z) = ecos. Let h(x) = f(f(q(=))). (a) Find a simplified formula for h(z)…

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Q: Find the value of k such that A is singular. 1 05 6 -1 0 4 5 k k. %3D

A: If the determinant of a matrix is zero then the matrix is singular.

Q: If X-P(A) such that, P(X = 1) = P(X = 2) then find A. %3D %D O None O A=V2 O A=V3 O A = 2

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Q: Which of the following is a counterexample of the quantification vx (|x| > 0)? A) 0 B) -1 1 D…

A: We will find out the required value.

Q: Which of the following statements involving sigma notation is always true? Ο Σακ- b) = Σ b-Σα ) k=1…

A: We can check which statement is correct.

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Q: Q1:Proof the following Limits : C. Ln=1n! e-n

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Q: The expansion of esin(x) is Select one: O a. x² x4 1+x+ ... 8 Ob. x² 1+x+- 2 - t... 8 c. x5 1+x+ 6.…

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A: Just substitute values of k as integers and you'll get your answer.

Q: Let A = {x x = 12k for some k E Z} Let B = { x | x = 4k for some k EZ} Prove that A CB.

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Q: T or F , prove your answer Suppose (an) is Cauchy and that for every n ∈ N, the interval (−1/n,…

A: Statement is TRUE By the ARCHIMEDEAN PROPERTY AND DEFINITION OF LIMIT.

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Q: Find the infimum, minimum, maximum and supremum of each of the following sets (write d.n.e. if it…

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Q: Let (an)1 be a sequence of positive real numbers: a, > 0. Suppose that Sn = > a; diverges. i=1 ai tn…

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Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.