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Compute the indicated limit.$$\text { (a) } \lim _{x \rightarrow \infty} \frac{\sqrt{x^{2}-1}}{x+3} \text { (b) } \lim _{x \rightarrow-\infty} \frac{\sqrt{x^{2}-1}}{x+3}$$

(a) 1(b) -1

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 4

Limits at Infinity, Infinite Limits and Asymptotes

Derivatives

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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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Hello. We have to find the limit Access tragedy Square root of X squared plus one upon express three here extends to the positive infinity. That means access greater than zero. So anyway, if we will take excess square outside from the square old, then it will be so. It's got a lot of access. Card will be X here because access greater than zero. Okay, so we can diet. Limit extends to infinity. X is square root of one plus one by X square upon one plus three y x before the limit here, then it will be square out of one plus when Brian 50 0 upon one. So it will be fun. Okay. For the part we hear excess tends to minus infinity. That means X is less than zero, so square root of X squared will be minus of X because if the square root of X described will always, we will always foster so access less than zero to minus of access posted. Okay, so we can die. Limit extends to a minus in 30 minus or fax the square root of one plus one by X square upon X one plus three y X Okay, So this ex this ex will be cancel out and limit exchange two months of infinity minus of the square root of one plus one by x Esquire upon one plus three y x Mm people the limit here. So it will be close to minus of one plus burn upon in pretty will be zero upon one plus in pretty will be zero. So it will be a quest to minus of this Kuroda ban that is minus of one. Right? I hope. Do you understood? Thank you.

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