For which pair of functions f(x) and g(x) below will the limit as x goes to infinity of the quotient of f of x and g of x equals 0 ?

a. f(x) = x3; g(x) = ln(x)

b. f(x) = x-2; g(x) = e-x

c. f(x) = x5; g(x) = ex

d. f(x) = ex; g(x) = x3

A function, an expression, rule, or law that defines the relationship between one variable (independent variable) and another (dependent variable) in mathematics. Functions are ubiquitous in mathematics and are essential for formulating the physical relationships of the natural sciences.

In mathematics, the set X-to-set Y function maps each element of X to exactly one element of Y. Set X is called the domain of the function, and set Y is called the codomain of the function. Functions were originally an idealization of how one variable depends on another.

A function is defined as a relationship between a set of inputs, each with its own output. Simply put, a function is a relationship between inputs, with each input associated with one output. Each function has a domain and a codomain or scope.

Exponentials grow faster than any power.

So, x⁵/eˣ-> 0

consider using l'Hospital's Rule. After 5 times, the limit is 120/eˣ -> 0

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For which pair of functions f(x) and g(x) below will the limit as x goes to infinity of the quotient of f of x and g of x equals 0 ? a. f(x) = x3; g(x) = ln(x) b. f(x) = x-2; g(x) = e-x c. f(x) = x5; g(x) = ex d. f(x) = ex; g(x) = x3

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What is a mathematical function?

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For which pair of functions f(x) and g(x) below will the limit as x goes to infinity of the quotient of f of x and g of x equals 0 ?

a. f(x) = x3; g(x) = ln(x)

b. f(x) = x-2; g(x) = e-x

c. f(x) = x5; g(x) = ex

d. f(x) = ex; g(x) = x3