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a_sh-v [17]
2 years ago
7

Use the appropriate substitutions to write down the first four nonzero terms of the Maclaurin series for the binomial (1+3x)^(-1

/3)
Mathematics
1 answer:
PolarNik [594]2 years ago
5 0

Answer:

First term=1

Second term=-x

Third term=2x^2

Fourth term =-\frac{28}{3!}x^3

Step-by-step explanation:

We are given that function

f(x)=(1+3x)^{-1/3}

We have to find the  first four non zero terms of the Maclaurin series for the binomial.

Maclaurin series of function f(x) is given by

f(x)=f(0)+f'(0)x+\frac{1}{2!}f''(0)x^2+\frac{1}{3!}f'''(0)x^3+....

f(0)=(1+3x)^{\frac{-1}{3}}=1

f'(x)=-\frac{1}{3}(1+3x)^{-\frac{4}{3}}(3)=-(1+3x)^{-\frac{4}{3}}

f'(0)=-1

f''(x)=\frac{4}{3}\times 3 (1+3x)^{-\frac{7}{3}}

f''(0)=4

f'''(x)=-4\times \frac{7}{3}\times 3(1+3x)^{-\frac{10}{3}}

f'''(0)=-28

Substitute the values we get

(1+3x)^{-\frac{1}{3}}=1-x+\frac{4}{2!}x^2+\frac{-28}{3!}x^3+...

(1+3x)^{-\frac{1}{3}}=1-x+2x^2+\frac{-28}{3!}x^3+...

First term=1

Second term=-x

Third term=2x^2

Fourth term =-\frac{28}{3!}x^3

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mafiozo [28]

The right answer is Option D.

Step-by-step explanation:

Let,

Kyle's money = x

Hayden's money = y

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Hayden has twice as much money in his savings account  as Jeremy.

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Keywords: Linear equations, division

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Which expressions are equivalent to 4^−2 ⋅7 ^-2?
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Answer:

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It can be 1/784,  28^(-2),  or  1/ (28^2)

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<span>v2 = u2 + 2as
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so 
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