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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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