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ira [324]
3 years ago
14

Over a three-day weekend, a rental car agency charges $65 to rent a car plus $0.30 for each mile traveled. If y represents the t

otal cost and x represents the total number of miles traveled, which function rule describes this pattern?
Mathematics
1 answer:
SOVA2 [1]3 years ago
3 0
Y=0.30x+65

point-slope form
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Let f(x)=\tan^{-1}x. Then f'(x)=\frac1{1+x^2}. Note that f(0)=0.

Recall that for |x|, we have

\displaystyle\frac1{1-x}=\sum_{n\ge0}x^n

This means that for |-x^2|=|x|^2, or -1, we have

\displaystyle f'(x)=\frac1{1+x^2}=\frac1{1-(-x^2)}=\sum_{n\ge0}(-x^2)^n=\sum_{n\ge0}(-1)^nx^{2n}

Integrate the series to get

f(x)=f(0)+\displaystyle\sum_{n\ge0}\frac{(-1)^n}{2n+1}x^{2n+1}

\implies\tan^{-1}x=\displaystyle\sum_{n\ge0}\frac{(-1)^n}{2n+1}x^{2n+1}

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