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4 years ago

Simplify {n - 1 - [n - 1 - (n - 1)]}.

Mathematics

2 answers:

adelina 88 [10]4 years ago

8 0

{n - 1 - [n - 1 - (n - 1)]}

=n - 1 - n + 1 + n - 1

=n -1

artcher [175]4 years ago

4 0

Don't forget the invisble negative ones to distriute
do inside to outside

{n-1-1[n-1-1(n-1)]}
do inside
{n-1-1[n-1-n+1]}
simplify inner parenthasees
{n-1-1[n-n+1-1]}
{n-1-1[0]}
multply
{n-1-0}
add
n-1-0=n-1

it is n-1 simplified

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<h3>4 Answers: A, B, C, D</h3>

=======================================================

Explanation:

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f(x) is decreasing. You can see this through a table of values or through a graph. For anything in the form 1/(x^k), it will be a decreasing function because x^k gets larger, so 1/(x^k) gets smaller, when x goes to infinity.

--------------------

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Let's integrate and find out

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So we have

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Meaning that,

$\displaystyle \int_{a}^{b} f(x) dx = g(b)-g(a)\\\\\\\displaystyle \int_{a}^{b} \frac{1}{x^6} dx = \left(-\frac{1}{5b^5}+C\right)-\left(-\frac{1}{5a^5}+C\right)\\\\\\\displaystyle \int_{a}^{b} \frac{1}{x^6} dx = -\frac{1}{5b^5}+\frac{1}{5a^5}\\\\\\$

If we plug in a = 1 and apply the limit as b approaches positive infinity, then the expression $-\frac{1}{5b^5}+\frac{1}{5a^5}$ will turn into $\frac{1}{5}$

Therefore,

$\displaystyle \int_{1}^{\infty} \frac{1}{x^6} dx = \frac{1}{5}\\\\\\$

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