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Compute the indicated limit.$$\text { (a) } \lim _{x \rightarrow \infty} \frac{2 x}{\sqrt{x^{2}+8}} \text { (b) } \lim _{x \rightarrow-\infty} \frac{2 x}{\sqrt{x^{2}+8}} \text { (Hint: } \sqrt{x^{2}}=-x \text { if } x<0 \text { ) }$$

(a) 2(b) -2

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 4

Limits at Infinity, Infinite Limits and Asymptotes

Derivatives

Campbell University

Baylor University

University of Michigan - Ann Arbor

University of Nottingham

Lectures

04:40

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.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

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01:15

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01:05

02:02

02:14

01:52

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00:40

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05:25

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01:32

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02:21

Hello. We have to evaluate this limits so we can try to limit extends to infinity. Two of X. So we will take a square. Yes. So we really there? Excess where it's comin from the denominator. So it will be one plus eight by Access Square. And from the and I discovered, will come out from the squirrels. It will be limit exchange two or still every day. So it will be both of eggs upon so scuttled off excess crime movie X plus one plus eight by Access Square. So it will be like this. Okay, limit extends to infinity to upon one plus eight by excess square and access tends to in twenties will put the limits. It will be too upon a spirit of luxury cars too. For the part B, the limit extends to minus of any pity to accept on a score YouGov excess car plus eight. So limit extends to minus of NPT. So we will take common also from the denominator X squared one plus eight by X squared. Ok? Yeah. So it will be cost too. Yeah. Mm. Yeah, Yes. Limit extends to minus of 20 to accident. Uh, square root of X squared will be miners of X because access tends to minus infinity access less than zero. Yes, it will be manners of X one plus eight by X square. So x cancel out okay. And we will put the limit here So it will be minus up to upon one plus eight by immediately with zero. So it will be close to minus up to, I hope Youll restaurant. Thank you for the part of it. Managed to it will be answered. And then for the party Do it answered. Thank you.

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