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Q: How many invertible functions exist with the signature Za→ Zb if a = b? %3D

A: To find the number of invertible functions from ℤa to ℤb. Given that a=b. Also ℤa has a elements.…

Q: theorem applies to the function f(x)= ln 21x on the given interval [1,e]. If so approximate the…

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Q: Prove by induction ? 뉴스금 i=

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Q: mental Theorem of Calculus to fin

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Q: Verify that the hypotheses of the Mean-Value Theorem are satisfied for f(x) = Vx +9 on the interval…

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Q: 1. State the Power Rule using both prime notation and Leibniz notation. What type of function does…

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Q: ne terminal point on th

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Q: A O Type here to search

A: Figure A is the required answer.

Q: – Using the Residue theorem evaluate dr +1

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Q: Use mathematical induction to prove Theorem 1 in Sec-

A: To prove that if b is an integer, where b>1, and n is a positive integer, then n can be expressed…

Q: Find out if it's divergent or covergent; Evaluate if covergent.

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Q: algebrail dosure OF F. Then th

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Q: 7. а) Prove that (ӑ — Б) х (ӑ+Б) %3 2ӑ х ѣ.

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Q: 39-40 Show that / is continuous on (-*, *). if 1 39. (x) -

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Q: 4. Prove Theorem 2.6.5.

A: Let p,q be any two distinct points on l. Let r be any point on l. Let m be the line containing p and…

Q: Prove by induction that -o( リ=0

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Q: limx-4 (15-8x) = -17 %3D

A: By using definition of limit

Q: Let n be natural number. Obtain formula DCn) I din Mcal, where Ø is the euler fi functiel and u is…

A: Please find step by step solution beow:

Q: Prove the Mean Value Theorem

A: The Mean value theorem can be proved considering the function h(x) = f(x) – g(x) where g(x) is the…

Q: verify that the function satisfies the hypotheses of the Mean Value Theorem on the given interval.…

A: Given function is, f(x)=x3

Q: strong induction ICt

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Q: Find x+1/x if x-1/x=sqrt(x)+ 1/sqrt(x) for x>1, x in R.

A: Find x+1x if x-1x=x+1x , x>1 , x∈R

Q: Explain the Central Limit Theorem and the Law of Large Numbers. There are 3 key points. Include the…

A: Law of large numbers(LLN). There are two main versions They are weak and strong LLN. Let…

Q: İnstructions: Show all your work Indicate your answers clearly.

A: Given, Tx=∑n=2∞1x-nπ+1nπ Extend the function Tx such that, Tx=1x-2π+12π+1x-3π+13π+.......... This…

Q: Let 3 2 1. Verify that I4 = A. Show all of your work. 2. Verify that Alz = A. Show all of your work.

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Q: Show also that the function ln(z) is unique up to addition of a constant 2πik, k ∈ Z.

A: ln(mn) =ln(m) +ln(n)  ln(am) =mln(a)

Q: What the Why? What theorem or rule su

A: f(x)=15xe-x         , x≥.5We have to find inverse of this function i.e, f-1(x)We know…

Q: 5. Let (1 2 3 A = 2 1 4 1 0 2 Find A-lif possible. If A-does not exist, explain why.

A: Given See the handwritten solution

Q: State the Fundamental Theorem of Algebra.

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Q: Coefficient of ' in the expansion of (1+x) (1+ x)* is

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Q: Essentials of DISCRETE MATHEMATICS

A: Hello. Since your question has multiple questions, we will solve first question for you. If you want…

Q: Continuous everywhere

A: The following are theorems, which you should have seen proved, and should perhaps prove yourself:…

Q: QI Determine a condition on |x - * 1| that will assure that 1 |x² – 1| < - 4

A: x2-1&lt;14Apply absolute rule:  If |u| &lt; a, a&gt;0 then -a &lt; u &lt;…

Q: Prove inf { ☆InEN}=0 sup { inen}= Prove sup?.

A: We have to prove that Inf { 1/n | n in N } = 0 Consider the set of all lower bounds, then 0 lies in…

Q: Proof that: 12-a) =r → そ= a+re

A: The solution is:

Q: Evaluate

A: As per the guidelines we can solve 3 parts only only. Please repost the same for more answers.

Q: d/dx (xnJn(x))=xnJn-1(x)

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Q: Strong induction is called strong because We are free to use all cases from base case to k We do not…

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Q: Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given interval.…

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Q: prove: f(x)=5x is continuous at x=2     note: please prove this in theorem format(two columns)

A: Consider the given function. y=5x Now, check the left first.…

Q: 1. State fundamental theorem of algebra and prove it by using Brouwer's Theorem.

A: Hey there. According to our policies we cannot answer more than one question at once. Since you have…

Q: alue of the funo 3) in the i

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Q: Give a proof of the Cauchy's Mean Value Theorem by considering the function F(x) = [f(b) – f(a)]g(x)…

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Q: O Principal Ideal Domain

A: Using theorem - Polynomial ring R[x] is pricpal ideal domain iff ring R is field itself Now given D…

Q: The Mean Value Theorem is used in many other theorems. Name three other theorems that require the…

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Q: how to prove a bijection

A: According to the definition of the bijection, the given function should be both, Injective-   to…

Q: Discuss the role of the Fundamental Theorem of Calculus in the proof of Green’s Theorem

A: To discuss the role of Fundamental theorem of calculus in the proof of Green's Theorem. Fundamental…

Q: sir 3rd rule with f

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Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!