Estimating tan(0.34x) Using Linearization of tan(πx) Near x = 1/3

Math Problem Statement

In this question, we will estimate the value of tan(0.34x) using the linearization of f(x) = tan(πx) at the nearby point x = 1/3.

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Calculus
Linearization
Derivative

f'(x) = d/dx [tan(πx)] = π sec^2(πx)
L(x) = f(a) + f'(a)(x - a) for linearization of f(x) at x = a

Linear approximation
Derivative of tangent function

Grades 11-12

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