84. a. Prove that e > 1 + x if x > 0. b. Use the result in part (a) to show that e 21+x + r.

Q: E [X - E ( X)]2 is Select one: O a. V( X) O b. E ( X) O c.E ( X2) O d. S. D(X)

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Q: Let f(x) = 3x – 1 and g(x) = x- 1. %3D Find (f o g)(-3). Then (f o g)(-3) =- (Simplify your answer.)

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Q: 12. Consider the algebraic expression E = (X + 3Y)*(a – 2b) draw a tree according to the equation!

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Q: 10. Give a combinatorial proof: For n ≥ 1 and k ≥ 1, (n)k = n · (n − 1)k-1.

A: To give: A combinatorial proof: For n≥1 and k≥1, k·nk=n·n-1k-1.

Q: The Lucas numbers L(n) have almost the same definition as the Fibonacci numbers: if n = 1 if n = 2…

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Q: solve 5.3 (using k(pi-k)/2) and setting k =pi/2 or by your own methods if you have easier ones

A: It is known to us that

Q: 5. Let r <0 be a negative real number. Use the Archimedean property to prove that there is an n EN…

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Q: re a deck of 10 cards numbered from 1 to 10. are grey and some are white. rds numbered 1, 2, 3, 5,…

A: The probability of an event is the number of favorable outcomes divided by the total number of…

Q: The number of visitors P to a website in a given week over a 1-year period is given by…

A: Given data :  P(t) = 117 + (t - 88)e0.02t 1 &lt; t &lt; 52 P'(t) = d/dt (117 + (t-88)e0.02t…

Q: 21.) lim √9th -3 h+o h

A: The given limit limn→09+n-3n

Q: 3. Prove or disprove the given statement. (a) If x e R, and x + 0, then 2x > x. (b) If n e Z*, then…

A: Given: (a) If x∈R, and x≠0,then 2x&gt;x (b) If n∈Z+, then 2n-1&gt;0

Q: 4. 15 – x| < 2

A: According to the guideline we should have been able to do only one question at a time #4

Q: Find a natural umber N such that if |a – 5| < e <1 then |a² – 25| < Nɛ.

A: According to our company policy, we are supposed to answer one question at a time. For the rest…

Q: 1 2. Prove that for r < 1, we have the following inequality: e* < I

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Q: The Maclaurin series for f(x) = x'e2) ts: -2)*x**2 (b) (a) (e) None kl k!

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Q: Monte Carlo integration is a method to numerically estimate integral like I(g) = Sa g(x)dx. The idea…

A: According to the law of large numbers, if X1, X2,…, Xn is a sequence of random variables with mean μ…

Q: 42. Let e = 1+ 1/1! + 1/2! + 1/3! + Show that if k is a positive integer, then kle is not an…

A: Given , e=1+11!+12!+13!+....we need to prove if k is a positive integerthen k!e is not an integer

Q: Evaluate the following [8(t+ 3)e¹dt 88

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Q: Let & be a real number defined by 1

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Q: Suppose P(A) = 0.4 and P(B) and B, show that 0.1 ≤ P(An B) ≤ 0.4. = 0.7. With no other assumptions…

A: We have given thatP(A) = 0.4P(B) = 0.7We have to show that0.1 ≤ P(AB) ≤ 0.4

Q: 1 2. Let e =. Determine the smallest choice of N > 0 such that N. 6 ' n(n + 1)

A: To determine the smallest choice.

Q: Find k such that P(-k &lt; Z &lt; k) = .6970  it might help to sketch the situation

A: To value of k can be determine as:By using Z-table,

Q: Cookies have to be in the oven between 8 and 12 minutes and brownies have to be in the oven between…

A: To Determine: when both are in the oven at the same time? Given: cookies have to be oven between 8…

Q: Find the least positive integer n such that x¹/(x² + 1) is O(x¹), and then show that it is O(x") for…

A: Given that the function is To find the least positive integers n such that the given function is and…

Q: (0.4) (2) ODN (0) Jo 0<- 0 1 172

A: The given problem is to solve the given partial differential equation with given initial conditions…

Q: s) Let f(x) 1 and g(x) 4 + 6. - х — 6 Then (fo g)(x) = (go f)(x) =

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Q: Suppose a € R. What are the possible values for [Q(a): Q(aº)]? Give examples with a6 EQ for each…

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Q: Let p denote 3x E Z such that P(x)" and q denote dx E R such that P(x)". Ğive a simple definition…

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Q: If E[X 4 and Var(X) 1, then E(1 + 5X)²] - and Var(2 + 4X)

A: GivenE(X)=4Var(X)=1

Q: 3. If а, 1000". Find N E I, the set of positive integers, such that an+1 N). n!

A: Given an=1000nn!. We have to find the N∈I such that an+1&lt;an, n&gt;N. For n=1 a1=100011! For n=2…

Q: Prove that: ā x (B x č) = (ã-č )b – (ã ·5 )ẽ

A: See the details solution in below

Q: Let x be a particular value of x². Find the value of such that the following is true. a. P(x² >x) =…

A: Note: Hi there! Thank you for posting the questions. As there are multiple sub parts, according to…

Q: (b) Prove the following statements: i. {x € R: [x – 4| = 2|| – 2} = {-6, 2} ii. {r €R : |x – 4| < x}…

A:

Q: etermine value of the smallest natural number N such that E1(-1)*- is within (0.001 of the value 2k…

A: Seriese approximation.

Q: Given g(x) = ex, evaluate each of the following. (a) g(In 3) (b) g[In (62)] (c) g In

A: The function is given by gx = ex To evaluate:  a gln3b gln62c gln1e2