taylor ln((x/2)^2+4^2)

Lösung

taylor

ln ((\frac{x}{2})^{2} + 4^{2})

4 ln (2) + \frac{1}{64} x^{2} - \frac{1}{8192} x^{4} + \frac{1}{786432} x^{6} - \frac{1}{67108864} x^{8} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 4 ln (2) + \frac{\frac{d}{d x} ( ln ( ( \frac{x}{2} ) ^{2} + 4 ^{2} ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( ln ( ( \frac{x}{2} ) ^{2} + 4 ^{2} ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ln ( ( \frac{x}{2} ) ^{2} + 4 ^{2} ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 4 ln (2) + \frac{0}{1 !} x + \frac{\frac{1}{32}}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{- \frac{3}{1024}}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{\frac{15}{16384}}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{- \frac{169114337280}{6 4 ^{8}}}{8 !} x^{8} + \dots

Fasse zusammen

= 4 ln (2) + \frac{1}{64} x^{2} - \frac{1}{8192} x^{4} + \frac{1}{786432} x^{6} - \frac{1}{67108864} x^{8} + \dots

\int_{- 2}^{2} \frac{1}{1 + x ^{2}} d x

d er i v a t i v e f (x) = \frac{2 x}{2 e ^{9 x}}

\frac{d}{d x} (ln (3 x - 5))

d er i v a t i v e y = \frac{( x - 2 ) ( x ^{2} + 2 x + 4 )}{x ^{3}}

d er i v a t i v e x^{2} + y^{2}