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3 years ago

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What is the value of the expression shown? 10 - 16:2

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1 answer:

krek1111 [17]3 years ago

3 0

Divide 16 by 2 first following PEMDAS.

10 - 8

Solve

2

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Q3) f(x) 2x^2 - 5x, g(x) = 3x^3 find g(4x)

mrs_skeptik [129]

Answer:

g(4x) = 192x^3

Step-by-step explanation:

For this problem, f(x) is irrelevant since we are simply are dealing with g(x). We will simply replace the value of x in g(x) with 4x. So let's do that.

g(x) = 3x^3

g(4x) = 3(4x)^3

g(4x) = 3(4^3)(x^3)

g(4x) = 3(64)(x^3)

g(4x) = 192x^3

Hence, g(4x) is 192x^3.

Cheers.

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Answer:

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Step-by-step explanation:

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Determine whether the following series converge or diverge

Mars2501 [29]

An alternating series $\sum\limits_n(-1)^na_n$ converges if $|(-1)^na_n|=|a_n|$ is monotonic and $a_n\to0$ as $n\to\infty$ . Here $a_n=\dfrac1{\ln(n+1)}$ .

Let $f(x)=\ln(x+1)$ . Then $f'(x)=\dfrac1{x+1}$ , which is positive for all $x>-1$ , so $\ln(x+1)$ is monotonically increasing for $x>-1$ . This would mean $\dfrac1{\ln(x+1)}$ must be a monotonically decreasing sequence over the same interval, and so must $a_n$ .

Because $a_n$ is monotonically increasing, but will still always be positive, it follows that $a_n\to0$ as $n\to\infty$ .

So, $\sum\limits_n(-1)^na_n$ converges.

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