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professor190 [17]
3 years ago
14

Two consecutive integers are such that 7 times the biggest and then added to the smallest equals

Mathematics
1 answer:
Arturiano [62]3 years ago
7 0

Answer:

61,62

Step-by-step explanation:

Let the smallest  number be x

Hence, the biggest number = x+1 [as it consecutive]

Hence,

7(x+1)+x=495

7x+7+x+495

8x=495-7

8x=488

x=61

Hence, smaller number=61, bigger number=62

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Int(1 \(1 + {e}^{x} )​
Andreyy89

Answer:

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Step-by-step explanation:

The first derivative of the denominator 1 + e^{x} is e^{x}. Rewrite the fraction to obtain that expression on the numerator.

\begin{aligned}\frac{1}{1 + e^{x}} &= \frac{1 + e^{x}}{1 + e^{x}} - \frac{e^{x}}{1+e^{x}}\\&=1-\frac{e^{x}}{1+e^{x}}\end{aligned}.

In other words,

\begin{aligned}\int{\frac{1}{1 + e^{x}}\cdot dx} &= \int{dx} - \int{\frac{e^{x}}{1+e^{x}}\cdot dx}\end{aligned}.

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\displaystyle \int{\frac{e^{x}}{1+e^{x}}\cdot dx} = \int{\frac{du}{u}} = \ln{|u|} = \ln{u} +C = \ln{(1+e^{x})}+C.

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