What is taylor (1+(1/2)*x)-4 ?

The answer to taylor (1+(1/2)*x)-4 is -3+1/2 x

taylor (1+(1/2)*x)-4

taylor

(1 + (\frac{1}{2}) \cdot x) - 4

- 3 + \frac{1}{2} x

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= - 3 + \frac{\frac{1}{2}}{1 !} x + \frac{0}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{0}{10 !} x^{10}

Refine

= - 3 + \frac{1}{2} x

t \to 0 lim (e^{5 t})

\frac{d}{d x} (e^{x^{2} - 3})

\frac{d}{d t} (10 sin (t))

\frac{d ^{2} y}{d t ^{2}} + 4 \frac{d y}{d t} + 4 y = 0

z \to 1 + i lim (z^{2} - 5 z + 10)