Question

Calculus early transcendental functions. Does the limit exit? What is the value of the limit?

Answer 1

The limit of the function exists

The value of the limit is 1/8

Explanations:

Given the limit of the function:

`\lim _(x\to1)((1+3x)/(1+4x^2+3x^4))^3`

In order to get the limit of the function, we will substitute x = 1 into the function;

`\begin{gathered} =((1+3(1))/(1+4(1)^2+3(1)^4))^3 \\ =((1+3)/(1+4(1)+3(1)))^3 \\ =((4)/(1+4+3))^3 \\ =((4)/(8))^3 \\ =((1)/(2))^3 \\ =(1)/(8) \end{gathered}`

Since the limit of the function results in a finite value, hence the limit exists.

The value of the limit is 1/8