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3 years ago

!!PLEASE HELP ME ASAP!!

Mathematics

1 answer:

saveliy_v [14]3 years ago

4 0

Answer:

The correct answer is c. 13/3

Step-by-step explanation:

In order to find this, we put -2/3 in for each x that we see and evaluate.

f(x) = 3x^2 - 6x - 1

f(-2/3) = 3(-2/3)^2 - 6(-2/3) - 1

f(-2/3) = 3(4/9) + 4 - 1

f(-2/3) = 4/3 + 3

f(-2/3) = 13/3

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Assuming the series is

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The series will converge if

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We have

$\displaystyle\lim_{n\to\infty}\left|\frac{\frac{x^{n+1}}{2(n+1)-1}}{\frac{x^n}{2n-1}}\right|=|x|\lim_{n\to\infty}\frac{\frac1{2n+1}}{\frac1{2n-1}}=|x|-\lim_{n\to\infty}\frac{2n-1}{2n+1}=|x|$

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If $x=1$ , then the series is a scaled harmonic series, which we know diverges.

On the other hand, if $x=-1$ , by the alternating series test we can show that the series converges, since

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and is strictly decreasing.

So, the interval of convergence for the series is $-1\le x$ .

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3 years ago

If a cup of coffee has temperature 97Â°C in a room where the ambient air temperature is 25Â°C, then, according to Newton's Law o

FinnZ [79.3K]

Answer:

The average temperature is $T_{a} = 81.95^oC$

Step-by-step explanation:

From the question we are told that

The temperature of the coffee after time t is $T(t) = 25 + 72 e^{[-\frac{t}{45} ]}$

Now the average temperature during the first 22 minutes i.e fro $0 \to 22$ minutes is mathematically evaluated as

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$T_{a} = \frac{1}{22} [25 (22) - 3240e^{[-\frac{22}{45} ]} - (- 3240e^{0} )]$

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