find a way to calculate accurate values of f(x) when x is near - f(x) = (radical(1+x^2) - 1)/ (x^2)

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.1: Techniques For Finding Derivatives
Problem 36E: Find all points on the graph of fx=x3+9x2+19x-10 where the slope of the tangent line is -5.
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find a way to calculate accurate values of f(x) when x is near -

f(x) = (radical(1+x^2) - 1)/ (x^2)

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why do you have to minus (x^2sinx)/(x-tamx) in the beginning?

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