taylor sqrt(x),16

Lösung

taylor

x, 16

4 + \frac{1}{8} (x - 16) - \frac{1}{512} (x - 16)^{2} + \frac{1}{16384} (x - 16)^{3} - \frac{5}{2097152} (x - 16)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 4 + \frac{\frac{d}{d x} ( x ) ( 16 )}{1 !} (x - 16) + \frac{\frac{d ^{2}}{d x ^{2}} ( x ) ( 16 )}{2 !} (x - 16)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ) ( 16 )}{3 !} (x - 16)^{3} + \dots

Evaluate Derivatives

= 4 + \frac{\frac{1}{8}}{1 !} (x - 16) + \frac{- \frac{1}{256}}{2 !} (x - 16)^{2} + \frac{\frac{3}{8192}}{3 !} (x - 16)^{3} + \frac{- \frac{15}{262144}}{4 !} (x - 16)^{4} + \dots

Fasse zusammen

= 4 + \frac{1}{8} (x - 16) - \frac{1}{512} (x - 16)^{2} + \frac{1}{16384} (x - 16)^{3} - \frac{5}{2097152} (x - 16)^{4} + \dots

f (x) = e^{10 x}

\frac{\partial}{\partial y} (x^{2} y^{2} e^{2 x y})

(x^{\frac{3}{2}})^{^{'}}

\frac{\partial}{\partial y} (ln (x^{2} + y^{2}))

ma c l a u r in ln (4 + x^{2})