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Popular >

taylor 80*22^{t/(20)}

Solution

taylor

80 \cdot 2 2^{\frac{t}{20}}

Solution

80 + (4 ln (11) + 4 ln (2)) t + \frac{ln ^{2} ( 11 ) + 2 ln ( 2 ) ln ( 11 ) + ln ^{2} ( 2 )}{10} t^{2} + \frac{4 ln ( 2 ) ln ( 11 ) ln ( 22 ) + 4 ln ^{3} ( 11 ) + 8 ln ( 2 ) ln ^{2} ( 11 ) + 8 ln ^{2} ( 2 ) ln ( 11 ) + 4 ln ^{3} ( 2 )}{2400} t^{3} + \dots

Solution steps

Apply the Taylor Formula

= 80 + \frac{\frac{d}{d t} ( 80 \cdot 2 2 ^{\frac{t}{20}} ) ( 0 )}{1 !} t + \frac{\frac{d ^{2}}{d t ^{2}} ( 80 \cdot 2 2 ^{\frac{t}{20}} ) ( 0 )}{2 !} t^{2} + \frac{\frac{d ^{3}}{d t ^{3}} ( 80 \cdot 2 2 ^{\frac{t}{20}} ) ( 0 )}{3 !} t^{3} + \dots

Evaluate Derivatives

= 80 + \frac{4 ln ( 11 ) + 4 ln ( 2 )}{1 !} t + \frac{\frac{l n ^{2} ( 11 ) + 2 l n ( 2 ) l n ( 11 ) + l n ^{2} ( 2 )}{5}}{2 !} t^{2} + \frac{\frac{4 l n ( 2 ) l n ( 11 ) l n ( 22 ) + 4 l n ^{3} ( 11 ) + 8 l n ( 2 ) l n ^{2} ( 11 ) + 8 l n ^{2} ( 2 ) l n ( 11 ) + 4 l n ^{3} ( 2 )}{400}}{3 !} t^{3} + \dots

Refine

= 80 + (4 ln (11) + 4 ln (2)) t + \frac{ln ^{2} ( 11 ) + 2 ln ( 2 ) ln ( 11 ) + ln ^{2} ( 2 )}{10} t^{2} + \frac{4 ln ( 2 ) ln ( 11 ) ln ( 22 ) + 4 ln ^{3} ( 11 ) + 8 ln ( 2 ) ln ^{2} ( 11 ) + 8 ln ^{2} ( 2 ) ln ( 11 ) + 4 ln ^{3} ( 2 )}{2400} t^{3} + \dots

Popular Examples

integral of 6/(9+6x)

\int \frac{6}{9 + 6 x} d x

derivative of sin(2x+cos(3x))

\frac{d}{d x} (sin (2 x) + cos (3 x))

tangent of f(x)=pi^{3x+3},\at x=2 tangent of

f (x) = π^{3 x + 3}, at x = 2

121y^{''}+88y^'+12y=0

121 y^{^{''}} + 88 y^{^{'}} + 12 y = 0

derivative of sqrt(4+cot^2(x))derivative of

4 + cot^{2} (x)

Frequently Asked Questions (FAQ)

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