Use the formula for the binomial series: m(m-1).--(m-k+1) k + m(m-1) 2 (1 + x)" 1+ mx + %3! 2! k! m(m-1)---(m-k+1) if 1+ ΣΕ |x| < 1 k=1 k! 1 to obtain the Maclaurin series for (1 +x)° 1- 9x + k! k=2 (k + 9)! 1 + 9! k=1 k! 8!2(-1) & + 8)! k! 1- 9x + k=2 (-1)k+1 (k + 8)! 10! 1 1- 9x + k! k=2 (k + 8)! 1 + 9x + > k! k=2

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A: solution given below

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A: Speed of the point = 60 mph time = 15 min ⇒time t=1560 hr. =14hr.

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A: follow the solution which is mentioned in step 2.

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A: We will find the mclaurian polynomial. 

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Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent. (-1)«...

A: Given:  By p-series, (1.1)nn8 is convergent. So, the given series is absolutely convergent.

Q: One measure of living standards in country A is given by the following formula. L(t) = 5 + 4 e 0.16t...

A: Given: One measure of living standards in country A is given by the following formula.L(t)=5+4e0.16t...

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A: the given curve,   x=13y y-3 where 1≤y≤2

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A: The given question can be solved as shown in step2.

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A: The given differential equation is; y'+y/x =y2x