Q. 50 - Calculus

Question

Use tables of values to make educated guesses for each of the limits in Exercises 39–52. 

$\underset{x\to \infty }{\lim }\left(1+\frac{1}{2x+1}+\frac{1}{x^2}\right)$

Step-by-Step Solution

Answer

The value of $\underset{x\to \infty }{\lim }\left(1+\frac{1}{2x+1}+\frac{1}{x^2}\right)$ is $1.$

Step 1. Given information.

The given function is $\underset{x\to \infty }{\lim }\left(1+\frac{1}{2x+1}+\frac{1}{x^2}\right)$.

Step 2. Value of the limit.

Consider the table,

 The value approaches to $1 as x\to \infty ,$

Therefore,

$\underset{x\to \infty }{\lim }\left(1+\frac{1}{2x+1}+\frac{1}{x^2}\right)=1$