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Anastasy [175]
1 year ago
14

NEED HELP QUICK !!! Find the value of side X ?

Mathematics
1 answer:
tankabanditka [31]1 year ago
7 0

a²+b²=x²

4²+3²= x²

16+9= x²

25= x²

V25= x

5= x

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Evaluate the following limit:
Makovka662 [10]

If we evaluate the function at infinity, we can immediately see that:

        \large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle L = \lim_{x \to \infty}{\frac{(x^2 + 1)^2 - 3x^2 + 3}{x^3 - 5}} = \frac{\infty}{\infty}} \end{gathered}$}

Therefore, we must perform an algebraic manipulation in order to get rid of the indeterminacy.

We can solve this limit in two ways.

<h3>Way 1:</h3>

By comparison of infinities:

We first expand the binomial squared, so we get

                         \large\displaystyle\text{$\begin{gathered}\sf \displaystyle L = \lim_{x \to \infty}{\frac{x^4 - x^2 + 4}{x^3 - 5}} = \infty \end{gathered}$}

Note that in the numerator we get x⁴ while in the denominator we get x³ as the highest degree terms. Therefore, the degree of the numerator is greater and the limit will be \infty. Recall that when the degree of the numerator is greater, then the limit is \infty if the terms of greater degree have the same sign.

<h3>Way 2</h3>

Dividing numerator and denominator by the term of highest degree:

                            \large\displaystyle\text{$\begin{gathered}\sf L  = \lim_{x \to \infty}\frac{x^{4}-x^{2} +4  }{x^{3}-5  }  \end{gathered}$}\\

                                \ \  = \lim_{x \to \infty\frac{\frac{x^{4}  }{x^{4} }-\frac{x^{2} }{x^{4}}+\frac{4}{x^{4} }    }{\frac{x^{3} }{x^{4}}-\frac{5}{x^{4}}   }  }

                                \large\displaystyle\text{$\begin{gathered}\sf \bf{=\lim_{x \to \infty}\frac{1-\frac{1}{x^{2} } +\frac{4}{x^{4} }  }{\frac{1}{x}-\frac{5}{x^{4} }  }  \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =\frac{1}{0}=\infty } \end{gathered}$}

Note that, in general, 1/0 is an indeterminate form. However, we are computing a limit when x →∞, and both the numerator and denominator are positive as x grows, so we can conclude that the limit will be ∞.

5 0
2 years ago
Which value of x is a solution to x2<br> = 16?
Helga [31]

Answer:

8

Step-by-step explanation:

if we take the 2 that is in the R.H.S and put it in L.H.S

it becomes 16÷2=8

8 0
3 years ago
St<br>Question 1<br>Calculate the derivative of y = f(x) = 3 x(4x + 7)<br>Your answer:<br><br>​
kondor19780726 [428]

Answer:

\frac{dy}{dx} = 24 x + 21

Step-by-step explanation:

<u><em>Explanation:-</em></u>

Given that the function

      y = f(x) = 3 x ( 4 x + 7)

     y  = 3 x ( 4 x + 7)  

    y = 12 x² + 21 x ..(i)

Differentiating equation (i) with respective to 'x' , we get

\frac{dy}{dx} = 12 (2x) +21 (1)

\frac{dy}{dx} = 24 x + 21

6 0
2 years ago
Please help, PLEASE will give brainlest answer
Korolek [52]

Answer:

SteAnswer:

y = 1/2x + 3/2

Step-by-step explanation:

Using the equation of the line

y - y_1 = m ( x - x_1)

First find the slope of the line

-2x + 4y = 8

It must be in this form

y = mx + C

4y = 8 + 2x

divide through by 4

4y/4 = 8 + 2x / 4

y = 8 + 2x/4

Let's separate

y = 8/4 + 2x/4

y = 2 + 1/2x

y = 1/2x + 2

Therefore, our slope or m is 1/2

Using the equation of the line

y - y_1 = m ( x - x_1)

With point (-5, -1)

x_1 = -5

y_1 = -1

y - (-1) = 1/2(x - (-5)

y + 1 = 1/2( x + 5)

Opening the brackets

y + 1 = x + 5 / 2

y = x + 5/2 - 1

Lcm is 2

y = x + 5 / 2 - 1/1

y = x + 5 -2/2

y = x +3/2

We can still separate it

y = x /2 + 3/2

y = 1/2x + 3/2

The equation of the line is

y = 1/2x + 3/2

The correct answer is A

brainliest?

8 0
3 years ago
Find (f•f)(0)<br> f(x) = x^2- 1<br> a. 1<br> b. 0<br> c. -8<br> d. -1
Fed [463]
B because anything multiplied by 0 is equal to 0.
3 0
3 years ago
Read 2 more answers
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