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Algebra
Pregunta

3. (a) Find the local quadratic approximation of \...

3. (a) Find the local quadratic approximation of \( \sqrt { x } \) at \( x _ { 0 } = 1 \) . (b) Use the result obtained in part (a) to approximate \( \sqrt { 1.1 } \) , and compare your approximation to that produced di- rectly by your calculating utility. [Note: See Example 

Answer

(a) 

\(f(x)= \sqrt{x}\\f'(x)= \frac{1}{2}x^{- \frac{1}{2} } \\f''(x)= - \frac{1}{4}x^{- \frac{3}{2} } \\\Rightarrow f(x_{0})= 1,f'(x_{0})= \frac{1}{2}, f''(x_{0})= - \frac{1}{4} \\\Rightarrow f(x)\approx 1+ \frac{1}{2}(x- 1)- \frac{1}{8}(x- 1)^{2}\)

Solución
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