All categories

3 years ago

The value of which of these expressions is closest to e?

Mathematics

2 answers:

irinina [24]3 years ago

6 0

Answer:

The correct answer option is $(1+\frac{1}{26} )^{26}$ .

Step-by-step explanation:

We are given a few mathematical expressions and we are to figure out which one among them has the value closest to that of e.

Using a calculator, we can check that $e$ = 2.718281828.

So let's evaluate each one of our given expressions to check which one of them is the closest to e:

$(1+\frac{1}{26} )^{26}=2.667784966$

$(1+\frac{1}{25} )^{25}=2.665836331$

$(1+\frac{1}{23} )^{23}=2.661450119$

$(1+\frac{1}{24} )^{24}=2.663731258$

Therefore, by looking at the above calculated values, we can conclude that the value of $(1+\frac{1}{26} )^{26}$ is the closest to the value of e.

Mazyrski [523]3 years ago

5 0

Answer:

A. (1 + 1/26)²⁶

Step-by-step explanation:

$e = \lim_{n \to \infty} (1+\frac{1}{n})^{n}$

and e ≈ 2.71828

The greater the value of n,the closer is the value of the expression (1+ 1/n)ⁿ to the value of e.

Of the given options, the greatest value of n = 26.

Hence (1 + 1/26)²⁶ is closer to the value of e.

You might be interested in

Tim has L inches of wire. He cuts the wire into pieces. The length of each piece is k inches. How many pieces of wire does Tim h

Yuki888 [10]

Answer:

L/k

Step-by-step explanation:

If Tim has a wire that is L inches long and each piece is k inches long, then you would divide the total length by the length of each individual to get the number of pieces.

So,

L/k

7 0

2 years ago

At a tennis event, 10% of a player's score is based on serves, 40% on return balls, and 50% on wins. Kyle makes 85% of his serve

ella [17]

The answer would be 74 I took the test :)

7 0

3 years ago

The function f(x) is defined below. What is the end behavior of f(x) ?

Dominik [7]

1363.xs and nun of yourrrt bennies

8 0

3 years ago

You buy 3 bags of sand and 5 bags of pea gravel for $26. In a second purchase (at the same prices), you buy 4 bags of sand for $

pickupchik [31]

Answer:

2z and 4y

Step-by-step explanation:

We first have to use the second purchase to figure this out, if 4 bags of sand is $8. We have to divide 8 by 4, which we get $2. We use this to find the bags of pea gravel. Since you bought 3 bags, 3 times 2 is 6. We subtract 6 from 26 leading to 20 dollars. We also buy 5 bags of pea gravel so we have two numbers, 20 and 5. We divide 20 and 5 and we get 4 dollars for 1 bag of pea gravel. If this is not what you meant I apologise.

6 0

3 years ago

Find the form of the general solution of y^(4)(x) - n^2y''(x)=g(x)

Dennis_Churaev [7]

The differential equation

$y^{(4)}-n^2y'' = g(x)$

has characteristic equation

r ⁴ - n ² r ² = r ² (r ² - n ²) = r ² (r - n) (r + n) = 0

with roots r = 0 (multiplicity 2), r = -1, and r = 1, so the characteristic solution is

$y_c=C_1+C_2x+C_3e^{-nx}+C_4e^{nx}$

For the non-homogeneous equation, reduce the order by substituting u(x) = y''(x), so that u''(x) is the 4th derivative of y, and

$u''-n^2u = g(x)$

Solve for u by using the method of variation of parameters. Note that the characteristic equation now only admits the two exponential solutions found earlier; I denote them by u₁ and u₂. Now we look for a particular solution of the form

$u_p = u_1z_1 + u_2z_2$