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Prove that $ \displaystyle \lim_{x \to 0}x^4 \cos \frac{2}{x} = 0 $.

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02:02

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 3

Calculating Limits Using the Limit Laws

Limits

Derivatives

Oregon State University

University of Nottingham

Idaho State University

Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

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.

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We have a question in this we need to prove that limit X approaches to zero. Access to the power four cost to buy stocks exit is really powerful because to buy X equal to zero, we have to prove it. So this could be done as limit X approaches to zero x rays to depart for In two. Cause I'm sorry and to limit X approaches to zero of course to buy X no cost to works. So for any value of this two by X, any value of two works cause will always be within the range minus one 21 So we can write it as limit X approaches to zero. X raised to the power for anything would win -1: one. Come on. This equal to 0, 0 into minus 121. So this will become zero, which is our right inside and improved. Thank you.

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