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Taylor Series

The Taylor series is a polynomial of infinite degree used to represent functions like sine, cube roots, and the exponential function. They're how some calculators (and Physicists) make approximations.

Local Linear Approximation


If \(f(1)=4\) and \(f'(1)=6,\) which of the following is the best local linear approximation for \(f(1.01)?\)

Estimate the value of \(\sqrt[3]{0.979}\) using local linear approximation for the function \(f(x)=\sqrt[3]{1+x}.\)

Use differentiation to estimate the value of \(\sqrt{16.5}\).

Estimate the value of \(\displaystyle \frac{6}{(1-x)^2}\) at \(x=0.02\) using local linear approximation.

What is the local linear approximation of the function \(f(x)=14x^3-5x\) near \(x = 1?\)


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