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Concept of tangent line approximation is important in calculus because it allows simplifying complex calculations and providing insight into the local behavior of functions. cards.algoreducation.com
This approximation is particularly useful when calculating function values that are difficult to compute directly, especially for nonlinear functions. library.fiveable.me For example, by looking at the tangent lines at various points, we can get a sense of the overall shape of the function and how it behaves near certain critical points. mathodics.com
Some other reasons why tangent line approximation is important: