tangent line approximation

In the previous post we have discussed about Newtons Law of Cooling Differential equation and In today's session we are going to discuss about tangent line approximation. The tangent line approximation in mathematics may be defined as approximating the value of any function that is hard to calculate with the help of the value of another function that is nearest to it.

To have more precise understanding of the tangent line approximation, let us take a very simple example. Consider a square root function f (x) that is f (x) = √x.

Now if we take x equal to 9 then f (9) = √9 which comes out as 3 and is very easily calculated. However if we consider x = 8.9 then f (8.9) = √8.9 and this cannot be calculated easily. Thus for f (8.9) = √(9 – 0.1), the value can be approximated with the help of the value which we got from f (9) = √9 = 3 ( since 0.1 is very small ).

Thus we can say that if the value of f (b + h) is hard to find whereas f ( b ) can be very easily calculated where | h | is very small (here the mod is taken as we need positive value of h) then the value of f (b+h) can be approximated with the help of the value of f (b). (know more about tangent line approximation, here)

Since in the example given above the value of h is equal to -0.1 thus the value of the function f can be approximated at the point (b+h) with the help of the tangent line to the graph of function f at the point b when | h | is very small.

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