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Levart [38]
3 years ago
8

(a) How is the number e defined? e is the number such that lim h → 0 e−h − 1 h = 1. e is the number such that lim h → 0 eh − 1 h

= 1. e is the number such that lim h → [infinity] eh + 1 h = 1. e is the number such that lim h → 0 eh + 1 h = 1. e is the number such that lim h → 1 e−h − 1 h = 1. (b) Use a calculator to estimate the values of the following limits to two decimal places. lim h → 0 2.7h − 1 h = lim h → 0 2.8h − 1 h = What can you conclude about the value of e? 0 < e < 1 2.7 < e < 2.8 0.99 < e < 2.7 0.99 < e < 1.03 1.03 < e < 2.7
Mathematics
2 answers:
Fed [463]3 years ago
7 0

Answer:

is the number such that lim h → [infinity] eh + 1 h = 1.

Step-by-step explanation:

The number e is known as the Euler's constant or Euler's number. The number  basically is a mathematical expression that is equal to the rational number 2.71828. In addition, it is also the base of the natural logarithm or the Naperian logarithms. It is the number that the natural logarithm is equal to one. In addition, it is the limit of :

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

as n approaches infinity.

The expression is calculated as a sum of the infinite series

e = \frac{1}{1!} = \frac{1}{1} + \frac{1}{1} + \frac{1}{1*2} + \frac{1}{1*2*3}+ ...

EleoNora [17]3 years ago
3 0

Answer/explanation

lim h → 0 (e^h − 1) /h = 1.

e is the number such that lim h → [infinity] e^(h + 1 )/h = 1.

e is the number such that lim h → 0 (e^h + 1)/h = 1.

e is the number such that lim h → 1 (e^−h − 1)/ h = 1

From the limits above, e is defined as a mathematical constant approximately equal to 2.71828.

The value of e is the base of the natural logarithm

(b) As h appoaches infinity, lim h → 0 (2.7^h − 1 )/h = lim h → 0 (2.8^h − 1 )/h = 2.72 to 2 decimal places.

It can be concluded that 2.70 < e < 2.80

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To find common denominators you must multiply both the numerator and the denominator by the same thing. Since your oposing fraction has a denominator of 5 you can know that a even number wont go in an odd number so take \frac{22}{5} and mutiply both numbers by 2 and get \frac{44}{10}. Then mutiply both numbers in \frac{7}{2} by 5 to get a common denominator.

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Step-by-step explanation:

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