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Popular >

taylor sqrt(x),\at 4

Solution

taylor

x, at 4

Solution

\frac{\frac{1}{2 at 4}}{1 !} (x - at 4) + \frac{- \frac{1}{4 ( at 4 ) ^{\frac{3}{2}}}}{2 !} (x - at 4)^{2} + \frac{\frac{3}{8 ( at 4 ) ^{\frac{5}{2}}}}{3 !} (x - at 4)^{3} + \frac{- \frac{15}{16 ( at 4 ) ^{\frac{7}{2}}}}{4 !} (x - at 4)^{4} + \dots

Solution steps

Apply the Taylor Formula

= at 4 + \frac{\frac{d}{d x} ( x ) ( at 4 )}{1 !} (x - at 4) + \frac{\frac{d ^{2}}{d x ^{2}} ( x ) ( at 4 )}{2 !} (x - at 4)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ) ( at 4 )}{3 !} (x - at 4)^{3} + \dots

Evaluate Derivatives

= at 4 + \frac{\frac{1}{2 at 4}}{1 !} (x - at 4) + \frac{- \frac{1}{4 ( at 4 ) ^{\frac{3}{2}}}}{2 !} (x - at 4)^{2} + \frac{\frac{3}{8 ( at 4 ) ^{\frac{5}{2}}}}{3 !} (x - at 4)^{3} + \frac{- \frac{15}{16 ( at 4 ) ^{\frac{7}{2}}}}{4 !} (x - at 4)^{4} + \dots

Refine

= \frac{\frac{1}{2 at 4}}{1 !} (x - at 4) + \frac{- \frac{1}{4 ( at 4 ) ^{\frac{3}{2}}}}{2 !} (x - at 4)^{2} + \frac{\frac{3}{8 ( at 4 ) ^{\frac{5}{2}}}}{3 !} (x - at 4)^{3} + \frac{- \frac{15}{16 ( at 4 ) ^{\frac{7}{2}}}}{4 !} (x - at 4)^{4} + \dots

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Frequently Asked Questions (FAQ)

What is taylor sqrt(x),\at 4 ?
The answer to taylor sqrt(x),\at 4 is