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Viktor [21]
3 years ago
15

Bobbie spends $9.50 on a pack of bulk candy that contains 100 pieces. How much does each piece of candy cost? Round the

Mathematics
1 answer:
True [87]3 years ago
5 0

I believe your answer should be $0.95

Of course, I could be wrong, and I apologise if I am.

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Use fundamental theorem of calculus to find derivative of the function LOOK AT PHOTO
kykrilka [37]

Let c > 0. Then split the integral at t = c to write

f(x) = \displaystyle \int_{\ln(x)}^{\frac1x} (t + \sin(t)) \, dt = \int_c^{\frac1x} (t + \sin(t)) \, dt - \int_c^{\ln(x)} (t + \sin(t)) \, dt

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\displaystyle \frac{df}{dx} = \left(\frac1x + \sin\left(\frac1x\right)\right) \frac{d}{dx}\left[\frac1x\right] - (\ln(x) + \sin(\ln(x))) \frac{d}{dx}\left[\ln(x)\right] \\\\ = -\frac1{x^2} \left(\frac1x + \sin\left(\frac1x\right)\right) - \frac1x (\ln(x) + \sin(\ln(x))) \\\\ = -\frac1{x^3} - \frac{\sin\left(\frac1x\right)}{x^2} - \frac{\ln(x)}x - \frac{\sin(\ln(x))}x \\\\ = -\frac{1 + x\sin\left(\frac1x\right) + x^2\ln(x) + x^2 \sin(\ln(x))}{x^3}

8 0
2 years ago
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