SOLUTION: When approximating secants to determine the slope of the tangent to a curve at a point P, why is it necessary to study cases for which Q approaches P from both sides of P? Explain

Question 1034463: When approximating secants to determine the slope of the tangent to a curve at a point P, why is it necessary to study cases for which Q approaches P from both sides of P? Explain with the help of an example.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
When approximating secants to determine the slope of the tangent to a curve at a point P, why is it necessary to study cases for which Q approaches P from both sides of P? Explain with the help of an example.
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Ans: Because the functi3n might be discontinuous at P so the limit
from one side may not equal the limit from the other side.
Ex::
f(x) = 2x + 3 for x<= 2
f(x) = 3x-1 for x > 2
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limit from the left = 2*2+3 = 7
limit from the right = 3*2-1 = 5
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Cheers,
Stan H.
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