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Evaluate the limit, if it exists.
$ \displaystyle \lim_{x \to -1}\frac{2x^2 + 3x + 1}{x^2 - 2x - 3} $
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02:41
Daniel Jaimes
Calculus 1 / AB
Chapter 2
Limits and Derivatives
Section 3
Calculating Limits Using the Limit Laws
Limits
Derivatives
Rr T.
February 18, 2021
Shouldn't you be using limit laws as discussed in chapter?
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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 develop it the limit of two X squared plus three X plus one over x squared minus two X minus three. As X approaches negative one know that if we directly substitute x equals negative one. We have two times negative one squared plus three times negative one plus one over have negative one squared minus two. Perhaps negative one minus three. This is equal to 0/0 which is indeterminant. And so we have to rewrite our function now. Not that we can write this into the limit as X approaches negative one of two, X plus one times expose one, this is all over x minus three times X plus one. And here we can reduce our functions since we can get rid of express one and we have limits as X approaches negative one of two, X plus one over x minus three. And so by direct substitution we have two times negative one plus one over negative one minus three. This is equal to negative one over negative four which is just 1/4. And so this is the value of our limits.
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