Prove that for any c>1 and any fixed p∈N, n^p/c^n→0.

Q: Prove that neQ

A: Given ddxxn=nxn-1

Q: Let A = {4n^2 + 1|n ∈ Z}. Show that A is a subset of Z but not equal.

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Q: Let x be the set of all positive integers and d(min) = | = - = | show that (x,d) is not complete

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Q: Let 2a4 + y* + 23 = 4 Then dz (1, 1) = 8/3 -8/3 none of the listed here 1

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Q: If n^2+6n+11 = x^2+y^2 for positive integer n, x and y prove [xy/2] is composite. Note: [t]…

A: Given :              n2+6n+11 = x2+y2              t ≤ t

Q: Show that it is not true that for every error 1/m there exists n such that |Ek=1 polt – r/(1 - r)| <…

A: We will show that for every m there does not exist any unique n that works for all r in (0,1)

Q: Let Z~ N(0, 1). Find P( - 2.4 < Z < 0.9). Submit Question

A: Solution-: In this case, Z is the standard normal random variable with μ=0 and σ=1. Mathematically,…

Q: Show dz 4 In= 는I미페 - for a<0. x <

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Q: Let x1, X . ,~ Bin( n,p) and p = . Find 1) A constant c such that E[c p ( 1 – p) ]= p(1- p). 2) Find…

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Q: Suppose that Z~N(0,1). Then find Pr(2.78 < Z < 2.84)

A: Given data, Z~N(0,1) That is Mean=0 Standard deviation=1 P(2.78 &lt; Z &lt; 2.84)=?

Q: et x + y+ z=5 where x, y, z E R. Prove that x² + y² + z² >

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Q: Show that the set A = {n^2/ (n+1): ne N} is unbounded in R.

A: To prove that the set A={n2n+1:n∈N} is unbounded in R,

Q: 3) Let f(x) = 1 + 3x on [-8, 2]. Find the number c that satisfies the mean value theorem. a) O C= b)…

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Q: A2

A: Consider the matrix A is, A=0100 Apply the condition, A2 = O. 0100·0100=0000 The matrix A is…

Q: Let D = {2, 4, 8) "For every z D, 2x¹ €

A: Given that set D = { 2, 4, 8}  And statement is  " For every x in D,   2| x". We need to check that…

Q: k* for some constant k". Lp.) Show that L(po)

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Q: Prove: If |S| = n then |P(S)| = 2^n

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Q: (п-1)! d) DE (x"-1nx)

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Q: Let X~N(10,9). Find P(X < 15.88).

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Q: Suppose that XnX in probability and Yn → Y in probability. Prove th

A: Given information: Xn→X in probability and Yn→Y in probability. That is, PXn-X&gt;ε→0, for every…

Q: 1. Let m*(A) = 0. Prove that for every B, m(BU A) = m*(B). %3D 2. Show that m" (A+ y) = m*(A). %3D…

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

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.