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Compute the indicated limit.$$\text { (a) } \lim _{x \rightarrow \infty} \frac{-5 x^{3}+x+3}{6 x^{2}+7} \text { (b) } \lim _{x \rightarrow-\infty} \frac{-5 x^{3}+x+3}{6 x^{2}+7}$$

(a) $-\mathrm{q}$(b) $\mathrm{q}$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 4

Limits at Infinity, Infinite Limits and Asymptotes

Derivatives

Campbell University

Oregon State University

Harvey Mudd College

Boston College

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.

01:05

Compute the indicated limi…

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00:46

Find the limits.$$…

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00:34

we have to solve these limits so we can added limit extends to infinity. We put the limit in this. This This is incredible Infinity. So we can write it. We will take excuse. Comin from the new letters will be minus five years. Yeah, when? Upon X square plus three y x Q accessible. We comment. We will be taken comin from the denominators. It will be seven by excess square. Okay, so by putting the values of the limit will be minus or five. Sorry, because in this limit, this is extreme. This extra square, so it will be equals two x minus of five plus one by every square. There's three y x Q upon six plus seven by X squared and B We put the limit exchange between 50 here. Then it will be cost too infinity or minus or five plus do you know plus zero of one six plus new. So the value of this limit believe minus of infinity. I hope you understood. Well, this is medicine Madison posted when we minus So this is the same function. So we can like it limit extent to minus organ pretty so we can add it. Mm. Like this. We can try to like this. Totally x multiplier. E minus five plus one Y x squared plus three y x cube upon six plus seven by X square. We put the limit here, and we will get minus of infinity minus of five plus zero. Plus zero upon six. No. Zero. Okay, this will be and finally was done. I hope you understand. Yeah. Thank you. This will be your answer for the party. This is the part B.

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