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Find the limit or show that it does not exist.
$ \displaystyle \lim_{x \to \infty} (e^{-x} + 2 \cos 3x) $
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02:51
Daniel Jaimes
Calculus 1 / AB
Chapter 2
Limits and Derivatives
Section 6
Limits at Infinity: Horizontal Asymptotes
Limits
Derivatives
Campbell University
University of Nottingham
Boston College
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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to evaluate the limits of erase the negative X. Plus to co sign of three X. As X approaches infinity, we first write this into the limit as X approaches infinity of erase the negative X. Plus you have a limit as X approaches infinity Of to co sign of three x. Now evaluating the first limit we have erased negative infinity Plus we have rewriting the second limit. That's too the limit. As X approaches infinity of Co sign of three x. Note that co sign function is a periodic function and we know that the value of co sign range is from negative 1 to 1. That means co sign of X. This is greater than or equal to negative one But this is less or equal to one. And because this is periodic The Value of Co Sign of three X. As X gets larger and larger Will either be -1 or one. and because the value of coastline of three x approaches to two values -1 or one. Then the value of the whole limit is indeterminate. That means it does not exist. In order to have a limit, we only need one value
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