I’m confused on this question

Answer:

[tex]\lim_{x \to 5}f(x)=-5\\\lim_{x \to 1^-} f(x)=3\\\lim_{x \to 1^+} f(x)=3\\\lim_{x \to 1} f(x)=4\\[/tex]

Step-by-step explanation:

[tex]\lim_{x \to 5}f(x)[/tex]

This means "the limit of f(x) as x approaches 5"

In this case, f(x) is a basic linear function while x > 1, so a limit is not necessary but it can still be used as it is here. For this one, you can just calculate f(5), and that is:

[tex]f(x)=5-2x[/tex]

[tex]f(5)=5-2(5)=5-10=-5[/tex]

[tex]\lim_{x \to 5}f(x)=-5[/tex]

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

[tex]\lim_{x \to 1^-} f(x)[/tex]

This one is a little different. It means "the limit of f(x) as x approaches 1 from the negative (left) direction"

The negative direction of course means x will be less than 1, so we'll use this function:

[tex]f(x)=4-x[/tex]

It's easier if you graph it, but you can also do it like this:

[tex]f(0)=4+0=4\\f(0.5)=4-0.5=3.5\\f(0.75)=4-0.75=3.25\\f(0.9)=4-0.9=3.1\\f(0.99)=4-0.99=3.01[/tex]

There's a clear pattern there. You can see that f(1) should be 3, but this function only applies while x is less than 1 so it can never reach 3. It will get infinitely close, and that can be shown with the limit:

[tex]\lim_{x \to 1^-} f(x)=3[/tex]

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

[tex]\lim_{x \to 1^+} f(x)[/tex]

This one works the same way, but from the positive (right) direction.

[tex]f(2)=5-4=1\\f(1.5)=5-3=2\\f(1.25)=5-2.5=2.5\\f(1.1)=5-2.2=2.8\\f(1.01)=5-2.02=2.98\\f(1.001)=5-2.002=2.998[/tex]

It will also get infinitely close to 3 when x = 1, but won't ever reach it because this function only applies when x is greater than 1.

[tex]\lim_{x \to 1^+} f(x)=3[/tex]

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

[tex]\lim_{x \to 1} f(x)[/tex]

Here, the function for x=1 is just:

[tex]f(x)=4[/tex]

It's given already, so the limit is just:

[tex]\lim_{x \to 1} f(x)=4[/tex]

Mr. Peate is building a rectangular fence around his house. The fence will be 32 feet long and 29 feet wide. What will be the perimeter of the fence? The perimeter will be ?​

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What is the probability that a point chosen at random in the rectangle is also in the blue triangle?

A triangle inside of a rectangle. The triangle is shaded and has a base of 5 inches and height of 4 inches. The rectangle is not shaded and has a height of 4 inches and length of 5 inches.
One-half
Four-fifths
1
2Simplify:

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(x-4)2 = 36
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0-4+ V(36)
O4 + V(36)
16+ (36)

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"Overnight parking on community streets is prohibited. For the purpose of this contract, 'overnight' will be defined as the hours between 11:00 p.m. and 4:00 a.m. The HOA will monitor overnight parking not less than once every calendar week with nightly patrols by community security.

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Because of the extremely low ground effects and body profile on his racing car, Peter is unable to drive his car off of the street and onto the driveway. He has parked on the street overnight for the past five weeks. He has received one written warning and one monetary fine from the HOA. What consequences should Peter expect after this week's security check?
a.
His car will be towed.
b.
He will receive another monetary fine.
c.
He will receive a monetary fine and his car will be towed.
d.
A "boot" will be place on his car to prevent him from driving it.

Use the similar triangles below to find the height of the tree

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-5/4 divided by 1 3/7

Show your work please

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A)
(-2,-1)
B)
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C
(4,-5)
D
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True or False

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________________

9:12=15:______

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​

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Quiz

2² =
4² =

use the method, no calculation ​