The nth root of n! a. Show that lim,(2n7)/(2n) = 1 and hence, using Stirling's approximation (Chapter 8, Additional Exercise 52a), that Vn! - for large values of n. b. Test the approximation in part (a) for n = 40, 50, 60, ..., as far as your calculator will allow.

Q: How 3 Find the absalute maxine and minima for the funCtion (4x-x) Cosy an the rectangular plate…

A: We have to find the absolute maximum and minimum.

Q: Q.2: Find horizontal and vertical . the asymptetes of ysflz)= 3x3.4%2, the finc tion

A: Given: y=fx=3x3-4x22x3-x

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A:

Q: 8. lim x - 4 + In (x – 4)

A:

Q: Question2. Construct piece-wise linear polynomials for function f(x) = over the interval (0,0.4]…

A: Given fx=11+x2  over the interval 0,0.4 with h=0.2. By piece-wise linear polynomials,there will be…

Q: 8.27) A saientist the numbber grows to the equation baderia ace NE)- Ae O· 1st where t ö measured i…

A:

Q: 6. The interval of increase for the parametric rational function y= k / (x - 3)^2, where ke R and k…

A: The given function is: k(x-3)2 The function is increasing for those values of 'x'

Q: a) Find the square root 14+ 4√6. b) If ƒ(r) = (2+1), show that ƒ(r) — ƒ(r+1) = r(r+1}(r+2). Hence,…

A: B. f(r) - f(r+1)

Q: 7. (a) Find the square root 14+4√6.

A: Note: Hi! Thank you for your question. As per the guideline we can solve one question at a time in…

Q: (g) y+1 = Yk + 6. %3D

A: The 1st order differential equation is            yk+12=yk+6

Q: Question 7. Let f(x) = 2x - √x. Find favg on the interval [1,4].

A:

Q: ections 17.2, 17.3) Find the work done by F(x, y) = −2yî – 2xĵ in moving a particle along a line…

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Q: Newton's Method requires applying the recursion formula: 2n+1= n f'(xn) a) Consider the function…

A:

Q: 3. (6れ)-) ANCTAN X (x+1) ² -y=ARCTAN

A: To expand the given function :

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A:

Q: .  (a) Sketch the graph of y = 2x2 over the interval [-1,1] (b) Let x be any point in the interval…

A:

Q: 2) Consider the function f(x) = -x + sin(-x) on the interval [0,1]. a) Approximate a root of f using…

A: Given function is              rewrite the above equation as               compare this with…

Q: Consider the function f(x)= x³ + 2x + 5. 1. Estimate the root to two significant digits using…

A: The bisection method uses the midpoint of an interval to perform the iterations to approximate the…

Q: 2. Use the Intermediate Value Theorem to find an interval of length one that contains a root of f(x)…

A: Given function is: fx=sin2x-x-ex. Using the Intermediate Value Theorem find an interval of length…

Q: 12 + U2 + PU2 U2 0, U1 > 0. U2 1- P 12 Thus, we get that U1-1 = 0, U2 - 12 = 0. So, U1 = l1 and U2…

A: GIVEN , =&gt; U1+PL1/U1+U2 +PL2/ U2 ≤L2+PU2/L2 +L1 +PU1/L1 NOW ,Taking Right side All to Left Side…

Q: Obtain a formula for the polynomial p(x₁) = yi p of least degree that takes these values: p'(x₁) = 0…

A:

Q: (a) Suppose dim V = 5 and S, TEL(V) are such that ST = 0. Prove that dim range TS 2. (b) Give an…

A: As per the question we are given a linear space V with dimension 5 and S, T are the linear…

Q: (c) 2y+1 - 5yk+1Yk + 2y% = 2,

A: (c) The given difference equation is 2y2k+1-5yk+1yk+2y2k=2

Q: F. (x) = (1) following Theo-pm by , indaction (1リ Prove The using Eqwatio, Theoranm, For um be-…

A:

Q: 1. Which of the following relations is FALSE. n+m A) (ab)" =a"b" B) C) (a")" 2. The equation of the…

A: To identify the false relation from give question.

Q: 11. If f(x)=-4¹, g(x)=√√x and h(x) = f(g(x)), determine h(-4)? ✓✓✓ Si7s100

A:

Q: Let fn(x) = n²x²(1 – x) on [0, 1]. Does lim,-00 So fn(x) exist?

A:

Q: Examl-Section 1: (a) Use appropriate Lagrange interpolating polynomials of degrees one (n-1), to…

A: Numerical analysis, Lagrange interpolation.

Q: If A(x)= 5x (1) - AP() = 1 1 + f² dt then:

A: Ax=∫05x11+t2dt

Q: Xi lim Σ n18 i=1 (x)² + 4 Δx, [1, 3]

A: Write integral as limit of a sum.