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Find the limit or show that it does not exist.

$ \displaystyle \lim_{x \to \infty} \sqrt{x^2 + 1} $

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00:56

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 6

Limits at Infinity: Horizontal Asymptotes

Limits

Derivatives

Harvey Mudd College

University of Nottingham

Idaho State University

Boston College

Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

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Find the limit or show tha…

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Evaluate the indicated lim…

To find the limit of the square it of expert plus one. As X approaches infinity, we first factor out the variable with the highest exponent. And so in here we have limit as X approaches infinity of the square it of x squared times one plus one over x squared. And then from here we simplify and we get limit as X approaches infinity of the square, the vex squared times the squares of one plus one over x squared. And then from here we get limit as X approaches infinity of the squared of x squared, that's just X Times the square root of one plus one over x squared. Now evaluating at infinity we have infinity times the square of one plus one over infinity. And since constant over infinity Approaches zero, then 1 over infinity will also approach zero. And from here we have Infinity Times The Square The one which is just infinity. And so this is the value of the limits.

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