Question

He was, without a doubt, the most prolific writer of mathematics of all time. Euler is credited as being the first mathematician to define function in the way we currently think of functions. In his book, Introductio in analysin infinitoriumin, he stated, “A function of a variable quantity is an analytic expression composed in any way whatsoever of the variable quantity and numbers or constant quantities.”
Based on what we know a function to be today, what did Euler mean by an analytic expression?

an expression formed with many variables and no numbers
an expression formed with many numbers and no variables
an expression formed from operations such as addition, multiplication, powers, and roots
an expression formed using only multiplication of a variable and a number

Answer 1

Based on what we know a function to be today, Euler mean an analytic expression "an expression formed from operations such as addition, multiplication, powers, and roots"

Euler's definition of a function

According to Euler, a function of a variable quantity is an analytic expression composed in any way whatsoever of the variable quantity and numbers or constant quantities.”

The function is. combination of expression which includes variables and constants using various operations such as roots, power and multiplication.

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