The answer to taylor 5^x is 1+ln(5)x+(ln^2(5))/2 x^2+(ln^3(5))/6 x^3+(ln^4(5))/(24)x^4+\ldots

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

taylor 5^x

Solution

taylor

5^{x}

1 + ln (5) x + \frac{ln ^{2} ( 5 )}{2} x^{2} + \frac{ln ^{3} ( 5 )}{6} x^{3} + \frac{ln ^{4} ( 5 )}{24} x^{4} + \dots

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( 5 ^{x} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( 5 ^{x} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 5 ^{x} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{ln ( 5 )}{1 !} x + \frac{ln ^{2} ( 5 )}{2 !} x^{2} + \frac{ln ^{3} ( 5 )}{3 !} x^{3} + \frac{ln ^{4} ( 5 )}{4 !} x^{4} + \dots

Refine

= 1 + ln (5) x + \frac{ln ^{2} ( 5 )}{2} x^{2} + \frac{ln ^{3} ( 5 )}{6} x^{3} + \frac{ln ^{4} ( 5 )}{24} x^{4} + \dots

y^{^{'}} - 2 x y = 0

\frac{d y}{d x} = \frac{1 + y}{x}

\int arccot (16 y) d y

x \to - 2 lim (- 3 x)

\int x + 3 d x

What is taylor 5^x ?
The answer to taylor 5^x is 1+ln(5)x+(ln^2(5))/2 x^2+(ln^3(5))/6 x^3+(ln^4(5))/(24)x^4+\ldots