When n is large, n! can be approximated by means ofthe expression√2πnnen called Stirling’s formula, where e is the base of naturallogarithms. (A derivation of this formula may be found inthe book by W. Feller cited among the references at theend of this chapter.)(a) Use Stirling’s formula to obtain approximations for10! and 12!, and find the percentage errors of these approximations by comparing them with the exact val-ues given in table Factorials and Binomial Coefficients of “Statistical Tables.”(b) Use Stirling’s formula to obtain an approximation forthe number of 13-card bridge hands that can be dealt withan ordinary deck of 52 playing cards.

Q: Bisection Solve for the root of f(x) = sin 4x if x₁ = −2 and XR = -1 Solve for the root of f(x) =…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: The rectangular cistern (storage tank for rainwater) shown has its top 15 ft below ground level. The…

A: According to guidelines we can do only first three sub parts thank you.We have to find the work and…

Q: 4. For n E N, n ≥ 2, find a formula for İ(¹-) j=2 and prove that your formula is correct. Note: This…

A:

Q: 21. Given that "( = "('3, the value of the integer n is 6 D 3

A: To find the value of n in the given problem, we use the definition of binomial coefficients.

Q: 20 ) Solve the following rational equation: = 3 x+3 2/X

A:

Q: 6 (iv) (v) (8) 5

A:

Q: Q2) Use rounding to 6 digits and compute each of the following: a) P(0.01), where P(x) = (e*…

A:

Q: 16П3 1 3 a 09 16П3 1 2п 3 (82)³/ (8r-2)3/2 3√8

A: a2=a

Q: The number z = −2 + 2i has modulus |z| = 2√2 and argument arg z =(5/4)π. But I have no earthly idea…

A: The objective of the question is to understand how to calculate the argument of a complex number…

Q: In the video, we introduced Newton's Method by considering the function )-x +1 and trying to…

A: To solve the part a, part b and part c. In the first part calculate the linearization of function…

Q: Determine the value of when y = 2/3 given that = 2-√√2²-5 and 5y=2+√√√2²-5. 0 3 03/2 01 O 1/2

A:

Q: Find all solutions of the given equation. (Enter your answers as a comma-separated list. Let k be…

A: It is trigonometric problem.

Q: (b) If f(r) = (+1), show that f(r)-f(r+1) = (+1)(+2). Hence, or otherwise, find Σr (r+1)(+2)

A:

Q: The most common approximation of nis the decimal 2.77. O True O False

A: The number π is an irrational number which means it cannot be represented as a ratio. But as it is…

Q: In calculating the approximate value of the fourth root of 624, which of the following approximation…

A:

Q: Use Right-endpoint Rule with n = 5 to approximate ²x x√x+2dx to 4 decimal places.

A: INTRODUCTION:  The height of the approximating rectangle is calculated using the right endpoint of a…

Q: 5x² √√3x² +1 dx

A:

Q: If In a = 2, ln b = 3, and ln c = 5, evaluate the following: a² b²c4 (a) In = (b) In √a²b²c4 =

A: To evaluate the given expression.

Q: а. Но: и 46 versus H1 :µ< 46. i ! < p-value < i ! tcritical i %D

A: a. The degrees of freedom is, df=n-1=17-1=16 The degrees of freedom is 16. The test statistic is…

Q: Put the function at-9bt in the = с form Q = kt and State the value of k. Assume a, b, & Care nonzero…

A:

Q: Q3-what is the importance of Stirling's formula. Derive 3 appr mathematical methods to have the…

A: The importance of Stirling's formula is that it allows us to calculate the factorial of a large…

Q: 2 ln (1+√√y) = 2 ln (1+√√x) + In C n{(1 + √y)²} = ln {C(1 + √@)²}

A: Given that 2 log 1+y=2log1+x+log C Here we need to explain the next steps.

Q: What are the values of the (6) Trig functions for "0" equal to 2250?

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Consider the expression. 7.20 x 10-5 = x(0.100 + æ)? You can solve for æ using a technique called…

A: We need to use iterative method to solve the given equation.

Q: Question 1 What is the exact value of csc 0_213 0 2√3 O 0-√√2 02 (167) ²

A: Let's find value of given trigonometric function.

Q: How large should n be to guarantee that the Trapezoidal Rule approximation to [(-2¹-…

A: and

Q: -(-6) ± V(-6)² – 4(3)(-3/4) +t = 3t2-6t - 2(3) 6 ± V36 + 9 =t = 6土V45 + t = 6+ 3/5 2士V5 +t = 2 +t =…

A: Explained below

Q: 1. Knowing that the sixth root of 64 is 2, estimate the sixth root of 68 by using the tangent line…

A:

Q: Choose the correct translation of: "Given any positive real number, its reciprocal is positive." A…

A:

Q: his doesnt inspire any confidence that it is correct. Question says S = sqrt(4n).(Xn-u) but this…

A:

Q: In real life computation, we can only round irrational numbers to certain number of decimal places,…

A: Given that error e=x-x´.

Q: a rational number y=10.01 b) Assume an integer, b=2 from 111 to 9 I assume from the range (0, ³/25).…

A: Given, X~Uniformx-32, x+32

Q: In this question, we will approximate 83 with a rational number. a)To use the linear approximation…

A: To solve the following problem

Q: sin + = √2 6 My thoughs sin π 4 ✓ why ? = √21232 f/2

A:

Q: Suppose the round-trip airfare between Boston and Orlando follows the normal probability…

A: Step 1: Given informationMean = $387.20Standard deviation = $68.50The distribution used is normal…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.