Who discovered calculus first? Who invented the notation 4?

Q: 3. Give an example of a mathematical theorem.

A: Since you have posted multiple question, we will solve the first one for you. To get the remaining…

Q: What are fermat numbers? What is the first fermat number?

A: In mathematics, a Fermat number, named after Pierre de Fermat, who first studied them, is a positive…

Q: State and prove the first fundamental the orem of calculus and its importance?

A:

Q: e Chinese remainder theorem.

A:

Q: List of formula for Integral calculus

A:

Q: What is the 5th term in the expansion of (x^3-1/x^2)^10?

A:

Q: Find Exponential Family 5-{r(r, 1),r > 0,2 is known }

A: The distributions that come under exponential distributions whose characteristics are dependent on…

Q: How is Green’s Theorem similar to the Fundamental Theorem of Calculus ?

A: How is Green’s Theorem similar to the Fundamental Theorem of Calculus ?

Q: 5. Determine the principal root of the 6th root of 2e^(jTT/2). Answer in exponential form. Round off…

A: To find 6th root of 2ejπ2

Q: Did Charles Babbage used calculus (integration) in inventing computer?

A: Yes

Q: Find the term indicated in the expansion .

A:

Q: Hi

A: Answers are correct and explained

Q: What Role do proofs play in mathematics?

A: Given: The objective is to explain the role of proofs in mathematics.

Q: Give two examples each of fundamental and derived quantities and their un

A: Fundamental quantities are independent physical quantity which not depend on each other. Derived…

Q: Use Newton’s method to approximate the given numbercorrect to eight decimal places. 100√100

A:

Q: What is the big-omega notation for 1* +2*++*?

A:

Q: What will the product of an even and odd number be? even or odd? Prove it with an example

A:

Q: 3x+2 + dt 1++5

A: Given  Fx=∫13x+2t1+t5dt

Q: A population of fruit flies is growing in such a way that each generation is 1.15 times as large as…

A: Given that: Population of fruit flies is 1.15 of the last generation in each new generation.Number…

Q: Who invented the algebra

A: Solution: The objective is to write the history of Algebra

Q: When are the two versions of Fundamental Theorem of Calculus helpfu

A: The first version of the fundamental theorem of calculus involves a variable like x so this will…

Q: Illustrate Rodrigues' Formula for Legendre Polynomials?

A:

Q: State the first part of the Fundamental Theorem of Calculus (FTC).

A: The first part of fundamental theorem of calculus states that -

Q: (2) Prove that (1+x)" > 1+nx for all x > 0 and n > 1.

A:

Q: Can you show it the "'short" way without using Pascal's method?

A: Given expression is: x-12x-24 We try to simplify it first: x-12x-24=x-12x-14=x-1·24·x-14=16x-15

Q: 28000 +38000 + 48000 + 58000 + 68000 Prove that 1 8000 is a multiple of 13 using Fermat's Little…

A: Given that                                 we have to prove that it is multiple of 13 by using…

Q: On a movie production lot, boxes of supplies are transported between two stations by a cable lift.…

A: To solve this question we will apply the balancing of the component of forces along vertical and…

Q: 1. Show that dr

A:

Q: Use Newton’s method to approximate the given numbercorrect to eight decimal places. 5√20

A: Consider  Find out the function and derivative.

Q: x+(x+1)+(x+2)+(x+3)+(x+4)=5x+10 What does this prove about the sum of these natural numbers?

A: The sum of the given equation is calculated as follows.

Q: How was the birth calculus attained?

A: Calculus was borned, rather developed independently by Newton and Leibniz, this marked as one of the…

Q: Use relevant definition(s) and theorem(s) to prove the fundamental theorem of calculus part 1.

A:

Q: a) ln n = O(n) b) ln n = O( sqrt(n) ) c) (ln n)^2 = O( sqrt(n) )

A: We know the following. Big O notation: We say that f(x)=O(g(x)) if there exists a positive real…

Q: Using mathem

A: To prove that P(n)=2(2n-1×3n+2) is divisible by 5 for every integer n≥1.

Q: Using modular arithmetic and Fermats Little Theorem, what is the remainder of (x-1)! when divided by…

A: Let   x  be prime. We need to find the remainder of  x - 1!  when divided by x. Since we know:   x -…

Q: State the fundamental theorem of arithmetic.

A:

Q: Explain in your own words what the Fundamental Theorem of Calculus says. Be sure to address both…

A:

Q: Use Pascal's Triangle to expand (1+2y)ª. (1+ 2y)*

A: Remember how the Pascal triangle work

Q: find the approximat

A:

Q: Derive the recursive formula using Newton-Raphson method for finding the reciprocal of a positive…

A:

Q: What is the coefficient of x squared in the expansion of (see attached image)

A:

Q: What Role do conjectures play in mathematics?

A:

Q: Discuss the two versions of the fundamental theorem of calculus

A: This the problem of Real Analysis, Theory of Reimann Integration.

Q: State the Fundamental Theorem of Arithmetic.

A: This is a B.sc course problem (Chapter- Integers),so I can do it in Advanced mathematics.

Q: Draw a number line on which adjacent tick marks are 0.1 unit apart and on which 0.003 can be plotted…

A:

Q: Expand (2r- 3) using Pascal's Triangle.

A: Expand (2x - 3)3 using Pascal triangle. According pascal triangle we use n value and take row of…

Q: A 500-gal tank initially contains 100 gal of brine containing 75 lb of salt. Brine containing 1 lb…

A:

Q: Vone of all. 2s (금+ In4).

A: Derivative: y=x2x+1We know,ddx(ax)=axlna