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2 years ago

State the Limits Rule and explain what it means

Mathematics

1 answer:

Evgen [1.6K]2 years ago

4 0

Answer:

The limit of a sum is equal to the sum of the limits.

Step-by-step explanation:

The limits of a constant times a function is equal to the constant times the limit of the function.

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Which of the following is a rational number <br> a.√5<br> b.π<br> c.1/2<br> d.√(77)

amid [387]

C. 1/2

the quotient of two integers

4 0

2 years ago

Please help! 20 points and brainly!!

boyakko [2]

Answer: 7/21 is the answer because 7 * 2 = 14 and 21*2=42

Step-by-step explanation:

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2 years ago

HELP!! Algebra help!! Will give stars thank u so much <333

Anna35 [415]

Answers:

Part a) $\bf{\sqrt{x^2+(x^2-3)^2}$
Part b) 3
Part c) 2.24
Part d) 1.58

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

Work Shown:

Part (a)

The origin is the point (0,0) which we'll make the first point, so let (x1,y1) = (0,0)

The other point is of the form (x,y) where y = x^2-3. So the point can be stated as (x2,y2) = (x,y). We'll replace y with x^2-3

We apply the distance formula to say...

$d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{(0-x)^2+(0-y)^2}\\\\d = \sqrt{(0-x)^2+(-y)^2}\\\\d = \sqrt{x^2 + y^2}\\\\d = \sqrt{x^2 + (x^2-3)^2}\\\\$

We could expand things out and combine like terms, but that's just extra unneeded work in my opinion.

Saying $d = \sqrt{x^2 + (x^2-3)^2}$ is the same as writing d = sqrt(x^2-(x^2-3)^2)

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

Part (b)

Plug in x = 0 and you should find the following

$d(x) = \sqrt{x^2 + (x^2-3)^2}\\\\d(0) = \sqrt{0^2 + (0^2-3)^2}\\\\d(0) = \sqrt{(-3)^2}\\\\d(0) = \sqrt{9}\\\\d(0) = 3\\\\$

This says that the point (x,y) = (0,3) is 3 units away from the origin (0,0).

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

Part (c)

Repeat for x = 1

$d(x) = \sqrt{x^2 + (x^2-3)^2}\\\\d(1) = \sqrt{1^2 + (1^2-3)^2}\\\\d(1) = \sqrt{1 + (1-3)^2}\\\\d(1) = \sqrt{1 + (-2)^2}\\\\d(1) = \sqrt{1 + 4}\\\\d(1) = \sqrt{5}\\\\d(1) \approx 2.23606797749979\\\\d(1) \approx 2.24\\\\$

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

Part (d)

Graph the d(x) function found back in part (a)

Use the minimum function on your graphing calculator to find the lowest point such that x > 0.

See the diagram below. I used GeoGebra to make the graph. Desmos probably has a similar feature (but I'm not entirely sure). If you have a TI83 or TI84, then your calculator has the minimum function feature.

The red point of this diagram is what we're after. That point is approximately (1.58, 1.66)

This means the smallest d can get is d = 1.66 and it happens when x = 1.58 approximately.

6 0

2 years ago

Which statement is true?

SVEN [57.7K]

Answer:

$y=log_{1} x$ is not a logarithmic function because the base is equal to 1.

Step-by-step explanation:

A logarithmic function is of the form: $y=log_{b}x$

For a logarithmic function to exist, we must fulfill certain conditions. The conditions are

i. The base, $b$ , is greater than 0. ${b>0)$

ii. The base, $b$ , is not equal to 1. $(b\ne 1)$

iii. $x$ must be greater than 0. $(x>0)$

Now, if we observe all the choices given, we conclude that the third choice is correct as the base there is 1. If base is equal to 1, then it violates the definition of logarithmic functions. So, the correct choice is:

$y=log_{1} x$ is not a logarithmic function because the base is equal to 1.

6 0

3 years ago

Read 2 more answers

Find the horizontal asymptote of of the graph of y=(-3x^6+5x+3)/9x^6+6x+4

NNADVOKAT [17]

Answer:

y = -1/3

Step-by-step explanation:

As x gets large, the value of the expression approaches the ratio of the highest-degree terms in numerator and denominator:

y = -3x^6/(9x^6) = -3/9

y = -1/3

5 0

3 years ago