Question

(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

Answer 1

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