Which are the solutions of the equation x^2+4x+4=25

Karo-lina-s [1.5K]

Answer:

The statement that correctly uses limits to determine the end behavior of f(x) is;

$\lim\limits_{x \to \pm \infty} \dfrac{7 \cdot x^2+ x + 1}{x^4 + 1}= \lim\limits_{x \to \pm \infty} \dfrac{7 }{x^2 }$ so the end behavior of the function is that as x → ±∞, f(x) → 0

Step-by-step explanation:

The given function is presented here as follows;

$f(x) = \dfrac{7 \cdot x^2+ x + 1}{x^4 + 1}$

The limit of the function is presented as follows;

$\lim\limits_{x \to \pm \infty} \dfrac{7 \cdot x^2+ x + 1}{x^4 + 1}$

Dividing the terms by x², we have;

$\lim\limits_{x \to \pm \infty} \dfrac{\dfrac{7 \cdot x^2}{x^2} + \dfrac{x}{x^2} + \dfrac{1}{x^2} }{\dfrac{x^4}{x^2} +\dfrac{1}{x^2} }= \lim\limits_{x \to \pm \infty} \dfrac{7 + \dfrac{1}{x} + \dfrac{1}{x^2} }{x^2 +\dfrac{1}{x^2} }$

As 'x' tends to ±∞, we have;

$\lim\limits_{x \to \pm \infty} \dfrac{7 + \dfrac{1}{x} + \dfrac{1}{x^2} }{x^2 +\dfrac{1}{x^2} } = \lim\limits_{x \to \pm \infty} \dfrac{7 + 0 + 0 }{x^2 +0 } = \lim\limits_{x \to \pm \infty} \dfrac{7 }{x^2 }$

However, we have that the end behavior of 7/x² as 'x' tends to ±∞ is 7/x² tends to 0;

Therefore, we have;

$f(x) \rightarrow 0 \ as \lim\limits_{x \to \pm \infty} \dfrac{7 }{x^2 }$

The statement that correctly uses limits to determine the end behavior of f(x) is therefor given as follows;

$\lim\limits_{x \to \pm \infty} \dfrac{7 \cdot x^2+ x + 1}{x^4 + 1}= \lim\limits_{x \to \pm \infty} \dfrac{7 }{x^2 }$ so the end behavior of the function is that as x → ±∞, f(x) → 0.

8 0

3 years ago

Find the slope given these two points: (0,1) and (-3, 6). Once

Naya [18.7K]

m=y2-y1/x2-x1

m = 6-1/-3-0

m=5/-3

the slope is negative because one of the number is negative.

4 0

2 years ago

Help plz!!!

AleksandrR [38]

Answer:

First graph

Step-by-step explanation:

First off, the graph opens up because <em>a</em> is positive. Second, the parent function of the quadratic graph is $\displaystyle y = x^2,$ and the greater the WHOLE NUMBERS [vertical stretch (<em>a</em>)] get, the slimmer the parabola gets, and the more you increase the DEGREE evenly [anything ending in 0, 2, 4, 6, and\or 8], the more flat, U-shaped the parabola becomes.

I am joyous to assist you anytime.

7 0

3 years ago

OPTIONS OVER HERE AND FOR A BETTER VIEW OF THE QUESTION LOOK AT THE PICTURE THANK YOU AND PLEASE HELP!!!

AlladinOne [14]

Answer:

a = 15

b = 7

c = 4

Step-by-step explanation:

Given in the question an expression $\sqrt[4]{15}^{7}$

This expression can be written as $15^{\frac{7}{4} }$

As we know that roots are most often written using a radical sign, like this, $\sqrt[n]{x}$ But there is another way to represent the taking of a root.

You can use rational exponents instead of a radical. A rational exponent is an exponent that is a fraction. For example, $\sqrt[n]{x}$ can be written as $x^{\frac{1}{n} }$

Secondly two powers having same base can be multiply

$x^{n}(^{m})=x^{nm}$

7 0

3 years ago

Simplify the following expression in your notebook. Select the correct answer. 7 - 3[(n 3 + 8n) ÷ (-n) + 9n 2]

Daniel [21]

Simplify the following:
7 - 3 (9×2 n + (3 n + 8 n)/(-n))

3 n + 8 n = 11 n:
7 - 3 (9×2 n + (11 n)/(-n))

(11 n)/(-n) = n/n×11/(-1) = 11/(-1):
7 - 3 (9 2 n + 11/(-1))

Multiply numerator and denominator of 11/(-1) by -1:
7 - 3 (9 2 n + -11)

9×2 = 18:
7 - 3 (18 n - 11)

-3 (18 n - 11) = 33 - 54 n:
33 - 54 n + 7

Add like terms. 7 + 33 = 40:
40 - 54 n

Factor 2 out of 40 - 54 n:

Answer: 2 (20 - 27 n)

8 0

3 years ago