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Compute the indicated limit.$$\text { (a) } \lim _{x \rightarrow 3^{+}} \frac{1}{(x-3)^{2}} \quad \text { (b) } \lim _{x \rightarrow 3^{-}} \frac{1}{(x-3)^{2}}$$

(a) $\mathrm{q}$(b) $\mathrm{q}$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 4

Limits at Infinity, Infinite Limits and Asymptotes

Derivatives

Harvey Mudd College

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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Hello. We have to find this limit. The limit extends to three plus one upon next Ministry. Holy square. As we can see, that X minus three has limit extends to three. It approaches to the zero X minus three. It tends to zero, so we can see that slimming. As you can see, that had extends to three. The ex ministry and the approaches to the zero and is greater than zero for X net three to the right. Okay, so the function increases with a long it is and bonded funds. And so we put the limit here. So it will be zeroes. Come with me in city. So from here here, X is near three to the lab. So we put the value of limits. What will be 31 is one is a three. So that is also in pretty. It is also 100,000. I hope I answered your question. Thank you.

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