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in this video were just going to go over a basic introduction into limits and how to evaluate them analytically and graphically so heres a simple example lets say if we want to find the limit as x approaches two of the function x squared minus four divided by x minus two so how can we do so well one way is to use direct substitution if we plug in two notice what will happen two squared is four four minus four is zero so zero over zero is undefined which we dont know what value that represents now sometimes you could find the limit by plugging a value thats close to two and thats what you want to do you want to plug in a number thats close to two but not exactly two so for example lets call this f of x so lets calculate f of 1.9 and lets see whats going to happen actually lets make it 2.1 so lets get a positive answer instead of a negative one two point one squared minus 4 thats about 0.41 and 2.1 minus 2 is 0.1 so this is going to be 4.1 now what if we pick a value that