Question: Show that lim n (1 + x/n) n = e x for any x > 0.

Show that lim nā†’āˆž (1 + x/n)n = ex for any x > 0.

Step by Step Solution

★★★★★

3.35 Rating (164 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Let m nx Then n xm an... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Precalculus Questions!

Q:

If a > 0; b > 0; show that lim (n + a)(n + b) - n) = (a + b)/2.

Q:

A sequence {an} is given by a1 = 2, an+1= 2 + an. (a) By induction or otherwise, show that {an} is increasing and bounded above by 3. Apply Theorem 11 to show that lim n an exists (b) Find lim n an.

Q:

Show that lim x2e-nx) = 0 and that lim (n2x2e-nx) = 0 for x R; x > 0.

Q:

6- X x1 Show that lim f(x) # 1. x-+1 2 by = X X No- O B. Ex 1, to show that lim f(x) #1, it is necessary to find a value of x for which | ( ) - 1| 27. x-+1

Q:

In this problem you will show that the sequence of functions \[f_{n}(x)=\frac{n}{\pi}\left(\frac{1}{1+n^{2} x^{2}} ight)\] approaches \(\delta(x)\) as \(n ightarrow \infty\). Use the following to...

Q:

34. A random variable X having density function f (x ) - de -1x ( 2x ) a -1 x > 0 [(a) is said to have gamma distribution with parameters a > 0, > > 0, where T(a) is the gamma function defined by...

Q:

Consider the standard normal distribution 1 e 2 du, TER, /2TT and let dn = (21nn - In Inn - In(47))1/2 and on = Prove lim n 1 - P(cnx + dn)] =e-, rER. You may find the following facts are useful: an...

Q:

Consider the standard normal distribution 1 e 2 du, TER, /2TT and let dn = (21nn - In Inn - In(47))1/2 and on = Prove lim n 1 - P(cnx + dn)] =e-, rER. You may find the following facts are useful: an...

Q:

Consider the standard normal distribution 1 e 2 du, TER, /2TT and let dn = (21nn - In Inn - In(47))1/2 and on = Prove lim n 1 - P(cnx + dn)] =e-, rER. You may find the following facts are useful: an...

Q:

Below are three formulae. Formula 1 E(X - X) (X - X) N- 1 Formula 2 E( X - X ) ( Y - ) N - 1 Formula 3 E( X - X ) ( Y - Y) (N - 1)(SD x) (SDy) In the space below: (1) Identify the statistic in each...

Q:

(i) P, = (ii) V = 0.5 (iii) x+= 1.1 Calculate i. Q2) Calculate d. A fully discrete whole life insurance is issued to (x). You are given: You are given: (i)x+ = 10.0 (ii) ,V, = 0.100 (iii) +1Vx =...

Q:

What is a permanent account? On which financial statement are permanent accounts reported?

Q:

Three Cheeses Pizza bought their current pizza oven two years ago for R10 500. It has one operating year remaining and a book value of R3 500. The owner could purchase a new oven for R2 200, but it...

Q:

Learn about the traditional and alternative consumer response hierarchies observed when consumers respond to messages, and realize their importance in promotional planning.

Q:

Suppose the line y = 5x 4 is tangent to the curve y = f(x) when x = 3. If Newtons method is used to locate a root of the equation f(x) = 0 and the initial approximation is x1 = 3, find the second...

Q:

For each initial approximation, determine graphically what happens if Newtons method is used for the function whose graph is shown. (a) x1 = 0 (b) x1 = 1 (c) x1 = 3 (d) x1 = 4 (a) x1 = 5 3.

Q:

Use Newtons method with the specified initial approximation x1 to find x3, the third approximation to the root of the given equation. (Give your answer to four decimal places.) 5. x + 2x - 4 - 0, x =...

Q:

Please list steps without using excel Historical demand for a company's product is as follows. (Please note this is NOT the same data set that you used in the naive approach and moving average...

Q:

Austin Grocers recently reported the following 2019 income statement (in millions of dollars): Sales $700 Operating costs including depreciation 500 EBIT $200 Interest 40 EBT $160 Taxes (25%) 40 Net...

Q:

Required information Problem 10-1A Plant asset costs; depreciation methods LO C1, P1 {The following information applies to the questions displayed below.] Timberly Construction makes a lump-sum...