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3 years ago

What is the limit as x is approaching 0 of the absolute value of x

1 answer:

6 0

Recall that, an absolute value expression is a piece-wise in effect, thus we'd check the single-sided limits,

$\bf \lim\limits_{x\to 0}~|x|\implies 
\begin{cases}
\lim\limits_{x\to 0^-}~-x\\\\
\lim\limits_{x\to 0^+}~+x
\end{cases}\implies 
\begin{cases}
0\\\\
0
\end{cases}\implies \lim\limits_{x\to 0}~|x|=0$

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What is the equation when y=5x+4 is reflected over the x-axis, y-axis & y=x?

tigry1 [53]

Answer:

A) $y=-5x-4$

B) $y=-5x+4$

C) $y=\frac{x-4}{5}$

Step-by-step explanation:

So we have the equation:

$y=5x+4$

Let's write this in function notation. Thus:

$y=f(x)=5x+4$

To flip a function over the x-axis, multiply the function by -1. Thus:

$f(x)=5x+4\\-(f(x))=-(5x+4)$

Simplify:

$-f(x)=-5x-4$

B) To flip a function over the y-axis, change the variable x to -x. Thus:

$f(x)=5x+4\\f(-x)=5(-x)+4$

Simplify:

$f(-x)=-5x+4$

C) A reflection over the line y=x is synonymous with finding the inverse of the function.

To find the inverse, switch x and f(x) and solve for f(x):

$f(x)=5x+4$

Switch:

$x=5f^{-1}(x)+4$

Subtract 4 from both sides:

$x-4=5f^{-1}(x)$

Divide both sides by 5:

$f^{-1}(x)=\frac{x-4}{5}$

And we're done :)

7 0

2 years ago

A map of a new dog park shows that it is triangular and that the sides measure 18.5m, 36.9m, and 16.9m. Are the dimensions corre

r-ruslan [8.4K]

In order to check whether the length of the sides are applicable to form a triangle is that we have to make sure that the sum of the length of two side should be greater than the third side.

18.5 m, 36.9 m, and 16.9 m
18.5 m < 36.9 m +16.9 m
36.9 m < 18.5 m +16.9 m
16.9 m < 18.5 m + 36.9 m

So the dimensions are correct!

5 0

3 years ago

Can someone help me with how to show the work.

mylen [45]

Answer:

x=2

Step-by-step explanation:

you can see explanation as attached file