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Find the indicated limit.$$\lim _{x \rightarrow 2}(7.1-3.4 x)$$

0.3

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 3

Limits and Continuity

Derivatives

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

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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This is a VD basic question based on limits. So we are given this expression 7.1 minus 3.4 x, and we have been given that the limit X is tending to to now, First of all, we have to check if we put into Can we get the answer? The answer over here is yes. If I simply put into this is going to be done 7.1 minus 3.4 and to do, which is nothing but minus 6.8. So this is going to give me 0.3. But what happens if the value is not in the domain, right? What happens if, after putting to this expression actually becomes undefined? And that guess what we do is we try to find limit extends two to minus, and then we find the limit of this expression when extends to two plus. And if both of these are equal, then we say that, yes, the limit exists. And whatever the answer that we get, the finite number that we say is our answer and which, if you do this, you will find that in both of these cases, the answer will come out to be close to 0.3. But luckily away here, after just putting in the value, we get our answer. So this is how we go about doing this question.

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