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3 years ago

The slope of the line y = 4x − 2 is:

Mathematics

1 answer:

Paladinen [302]3 years ago

6 0

Answer: m = 4

Step-by-step explanation: This is a linear equation.

Linear equations can be written in the form y = mx + b where

the multiplier, m, represents the slope of the line and the b

or the constant term represents the y-intercept of the line.

So the slope of this line is simply the multiplier

which is the coefficient of the x term which is 4.

The variable that's used to represent slope is m.

So we say that m = 4.

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3 years ago

Given g(x) = 10x + 2, find x when g(x) = 2.

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Answer:

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Step-by-step explanation:

We are given:

g(x) =10x +2

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3 years ago

Find the number to which the sequence {(3n+1)/(2n-1)} converges and prove that your answer is correct using the epsilon-N defini

Nat2105 [25]

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Now, for the limit as $n\to\infty$ to be equal to $\dfrac32$ is to say that for any $\varepsilon>0$ , there exists some $N$ such that whenever $n>N$ , it follows that

$\left|\dfrac{3n+1}{2n-1}-\dfrac32\right|$

From this inequality, we get

$\left|\dfrac{3n+1}{2n-1}-\dfrac32\right|=\left|\dfrac{(6n+2)-(6n-3)}{2(2n-1)}\right|=\dfrac52\dfrac1{|2n-1|}$
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$\implies2n-1\dfrac5{2\varepsilon}$
$\implies n\dfrac12+\dfrac5{4\varepsilon}$

As we're considering $n\to\infty$ , we can omit the first inequality.

We can then see that choosing $N=\left\lceil\dfrac12+\dfrac5{4\varepsilon}\right\rceil$ will guarantee the condition for the limit to exist. We take the ceiling (least integer larger than the given bound) just so that $N\in\mathbb N$ .