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Find the indicated limit.$$\lim _{x \rightarrow 0} \frac{x^{2}+5 x+2}{2 x^{2}+2 x+1}$$

2

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 3

Limits and Continuity

Derivatives

Oregon State University

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Idaho State University

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.

01:22

Find the limits.\begin…

01:06

Find the limits.$$\lim…

01:26

Find the indicated limit.<…

02:21

Find the limits$$\lim …

00:20

01:15

01:48

Find the limit, if it exis…

00:47

in this problem, we had to find the limit off. X approaches to zero off the given rational function. Extra care plus five eggs plus two bond two. X girl Bless two eggs The last one here. The given rational function is defined for all real numbers, so we can apply the limit as X approaches to zero with girls. Zero scare less five times zero less too bond to into zero square plus two into zero last one, we have zero plus zero plus two upon zero plus zero plus one. Finally, we have plus tau, which is a required limit for the given rational function.

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