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(a) Show $\lim _{x \rightarrow 2} x^{2}=4 .$ How close to 2 should the $x$ -values be chosen to guarantee that the $y$ -values are (b) between $4-0.1$ and $4+0.1 ?$(c) between $4-.01$ and $4+.01 ?$ (d) between $4-\epsilon$ and $4+\epsilon ?$ where $\epsilon$ is any positive number less than 4.

(c) $\bar{x}-2^{-6} \min (\sqrt{4-\mathrm{P}}, \sqrt{4+\mathrm{P}})$ or $\bar{x}-2^{-} 6 \min (1, \mathrm{P} / 3)$ amongother choices

00:51

Suman Saurav T.

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 3

Limits and Continuity

Derivatives

Oregon State University

Harvey Mudd College

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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To evaluate that extends to full minus of british individually? That's fine. Let this limit peak when you do and as we know that we didn't need your function. It extends to my needs well minus the value. The greatest individual function will be willing to treat. So this implies that the limit will be willing to three. This one that is the value that is equal or agencies. And the correct answer is option B. That is the limit it extends to full miners of greatest individual. Okay, This one is between and two forests answer.

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