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Find the indicated limit.$$\lim _{x \rightarrow 3} \frac{x^{2}-7 x+12}{x-3}$$

-1

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 3

Limits and Continuity

Derivatives

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.

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in this problem, we had to find the indicator limit for the given rational function. We just limit off. Ex occur minus seven x less to help a bond X minus three as X approaches to three here when we apply as X approaches to three, the denominator vanish 20 which becomes undefined. Therefore, before going toe, apply the limit. We will simplify the given rational function because we have removable non continue t So let us simplify the given rational function. Then we will apply. The limit is the new miniter off the given function can be faked rice as X minus tree into X minus four, divided by X minus three So we can cancel are the common factor from numerator and denominator. We have lim X approaches to three Off X minus four. Now we can apply the limit as X approaches to three. We have as extra punches to three. We have free minus four. There goes minus one, which is the required limit off the given

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