Limits of Functions.

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Presentation transcript:

Limits of Functions

For the above function if we were to put in x = 2 then we would have an undefined function

x (x^2-4)/(x-2) 3 5 2.5 4.5 2.1 4.1 2.05 4.05 2.01 4.01 2.005 4.005 2.001 4.001 2 #DIV/0! 1.999 3.999 1.995 3.995 1.99 3.99 1.95 3.95 1.9 3.9 1.5 3.5 1 From above 2 and below 2 the value of f(x) is getting very close to 4 so 4 is its limit.

4 2

does not exist because the left and right hand limits do not match! 2 1 1 2 3 4 At x=1: left hand limit right hand limit value of the function

because the left and right hand limits match. 2 1 1 2 3 4 At x=2: left hand limit right hand limit value of the function

because the left and right hand limits match. 2 1 1 2 3 4 At x=3: left hand limit right hand limit value of the function