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Find the indicated limit.$$\begin{aligned}&f(x)=\frac{|x|}{x}, \text { determine }(a) \lim _{x \rightarrow 4} f(x)(b) \lim _{x \rightarrow-4} f(x)(c) \lim _{x \rightarrow-a} f(x)\\&\text { (d) } \lim _{x \rightarrow a} f(x) \text { where } a>0\end{aligned}$$

(a) 1(b) -1(c) -1(d) 1

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 3

Limits and Continuity

Derivatives

Missouri State University

Campbell University

Baylor University

Idaho State University

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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thanks. This problem. Yeah. We have to find the limit off the function. Therefore, X is equal to absolute value off exit upon X in first part, in what we have to find, limit off a four eggs as X approaches to plus four. So let us apply that given limit for the U. N. Function limit as X approaches to zero. The function is absolute value off X, A bond eggs. Now we can directly apply the limit. That is absolute. Where you are four upon for so absolutely or forties for divided by four. So the question will be one in part. We off this problem. We have to find the limit off f off eggs as X approaches to minus four. So what does? Why the limit? Uh huh. Absolute value off X upon eggs as X approaches to minus for. So we have absolutely I do off. Just apply The limit divided by minus for is absolutely off. Minus four is will be plus for, by definition, off the absolute value a bond minus for on being divided for by minus For we have questioned minus one. Now, in part C off this problem, we have to find the limit. X approaches to minus a off a pall ex. So let us apply the limit. X approaches to minus a off absolute value off X, up on X. So from here we have. After applying the limit, we have minus absolute radio off minus anybody by minus a. So again, we have anybody'd by minus a which is equal to my next one in body or this problem off this problem. We have to find the limit off X approaches toe, uh, off F off X. So we have limit X approaches toe a off absolute value off except on eggs. So applying the limit as X approaches toe rehab? Absolutely. You off air upon a which is which will be equal to any worried by that Gives what? So hence these air that required the gated limits which we have to find for the given function

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