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Let $f(x)=\frac{x^{2}-9}{x-3},$ determine each of the following limits: $(a) \lim _{x \rightarrow-3} f(x)$(b) $\lim _{x \rightarrow 3} f(x)$Let $f(x)=\frac{x^{2}-9}{x-3},$ determine each of the following limits: $(a) \lim _{x \rightarrow-3} f(x)$(b) $\lim _{x \rightarrow 3} f(x)$

(a) 0,(b) 6

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 3

Limits and Continuity

Derivatives

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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.

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in this problem, we have to find the limit off. F Off X is equal to ex. Occur minus nine bond X minus tree Before going to applying the limits, let us simplify the given rational function as X secure minus nine and can be faked. Rise as X plus three into X minus three, divided by X minus three So we can cancel common factors from numerator and denominator. Finally, we have f off X is equal to X plus three. No, now we will find the limit in part A. We have to find the limit off X approaches to minus tree off F off X, which is which will be equal to limit X approaches to minus three Europe Off Axis X plus three. Now by applying limit rehab. Bless X by ministry. We have minus tree plus three, which is equal to zero. In part B. Off this problem, we had to find the limit off X approaches to tree off F off X. So we have limit X approaches to three F off Axis X plus three by playing limited X approaches. Toe plus three we have three plus three, which is equal toe six and plus six and zero are the required limits off the given

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