1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Arada [10]
3 years ago
11

The value that (1 plus StartFraction 1 Over n EndFraction )Superscript n1 1 nn approaches as n gets larger and larger is the irr

ational numberTrue/False
Mathematics
1 answer:
WINSTONCH [101]3 years ago
8 0

Answer:

Step-by-step explanation:

Given that,

y=(1 + 1/n)ⁿ

As n goes larger 1/n approaches 0

y=1^∞

Then, this is the indefinite,

So let take 'In' of both sides

y=(1 + 1/n)ⁿ

In (y) =In ((1+1/n)ⁿ)

From law of logarithm

LogAⁿ=nLogA

Then, we have

In(y)= In ((1+1/n)ⁿ)

In(y)= n•In (1+1/n)

This can be rewritten to conform to L'Hospital Rule

In(y)= n / 1 / In(1+1/n)

As n approaches infinity

n also approaches infinity

And In(1+1/n) approaches 0, then, 1/In(1+1/n) approaches infinity

Then we have another indeterminate

Then, applying L'Hospital

Differentiating both the denominator and numerator

The differential of 1/In(1+1/n)

n^-2In(1+1/n) / (In(1+1/n))²

1 / n²In(1+1/n)

Then, apply L'Hospital

In(y) = 1/ n²In(1+1/n)

As n tends to infinity

In(y)= 0

Take exponential of both sides

y=exp(0)

y=1

As n goes larger the larger the irrational number but when n goes to infinity then the irrational number goes to 1

You might be interested in
Shane is goin to the movies with his friends.His mom give them $15.00 to spend on snacks. Drinks cost $2.00 each and candy cost
RUDIKE [14]
<h3>- - - - - - - - - - - - - - - ~<u>Hello There</u>!~ - - - - - - - - - - - - - - - </h3>

➷ Simply divide the values:

15/2 = 7.5

Shane can buy 7 drinks

OR

15/3 = 5

Shane can buy 5 candies.

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ Hannah ♡

3 0
3 years ago
Is 3/4 greater than 7/8?
yKpoI14uk [10]
3/4 = (2*3) / (2* 4) = 6/8

7/8.

Is 3/4 greater than 7/8? 
Is like asking is 6/8 greater than 7/8?  Because 3/4 is equivalent to 6/8.

The answer is No.
3 0
3 years ago
Read 2 more answers
Multiply the equation 2x+2y=8 by 3. Does the equation have the same solution set?
stepan [7]

Multiply the equation:

2x+2y=8 \mapsto 6x+6y=24

The solution set is the same, because multiplying both sides of an equation by a non-zero number doesn't change the solution set. In fact, if you rewrite the equation as

2x+2y-8=0

Multiplying this by 3 (or whatever number, for all it matters) gives

3(2x+2y-8)=0

Now, a product is zero if and only if at least one of the factor is zero. So, either 3=0 or 2x+2y-8=0

Since the first is clearly impossible, the second one must be true, which is the original equation.

3 0
3 years ago
A population of 42 fruit flies has increased
Alex777 [14]
Multiply 42 times 150 percent or 42×1.5 which would be 63
7 0
2 years ago
Find the average rate of change of this function:
Phoenix [80]

Answer:

A slope of the line over the interval of [-6, -1] is ⅕ as illustrated in the graph above

7 0
3 years ago
Other questions:
  • How to find the 84% of 175
    12·2 answers
  • Beth read a total of 12 books over 7 months.
    6·2 answers
  • How do i simplify this
    12·1 answer
  • What is the measure of the sum of all angles in a regular dodecagon (12 sides)? What is the measure of one of its interiors angl
    11·1 answer
  • A paint store makes three batches of a color called Sunset Orange using the recipe
    15·2 answers
  • -<br>(23)<br>x +. 8<br>1 - 2x = 8 + x<br>5<br>3<br>-<br>5x - 1<br>24​
    15·1 answer
  • I will mark brainiest please please answer 30 points
    11·1 answer
  • Given sin (-∅) = -1/4 and tan∅ = √15/15.<br> What is the value of cos∅?
    13·1 answer
  • In attempting to create a reduced row echelon matrix, DeShawn got the following matri
    13·2 answers
  • Eight burgers and three orders of fries cost $79.49. Six orders of fries and twelve burgers cost $125.82.Find the price of one b
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!