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2 months ago

Question 1(Multiple Choice Worth 2 points)

Mathematics

2 answers:

babunello [11.8K]2 months ago

5 0

Here are 3 questions with their respective answers.

1) Find

$\lim_{x \to \ 2^+} f(x)$

Answer: 4.

Explanation:

This expression indicates the limit as the function f(x) approaches 2 from the right side.

You should apply the function (the line) from the right side of 2 and get as close to x = 2 as you can.

That line has an open circle at y = 4, which is the limit we are looking for.

2) Analyze the graph to see if the limit exists.

Answer:

$\lim_{x \to \ 2^-} f(x) = 3$

$\lim_{x \to \ 2^+} f(x)=-3$

To find each limit, utilize the function approaching from the direction of x.

It's important to note that since the two limits differ, it is concluded that the limit of the function as x approaches 2 does not exist.

3)
Answer: -1

$\lim_{x \to \ 3^-} f(x) = -1$

To determine the limit as the function approaches 3 from the left, follow the line ending with an open circle at (3, -1).

Hence, the limit is -1.

tester [12.3K]2 months ago

4 0

Answer:

The first number is 4 and the second one is 3; -2

Step-by-step explanation:

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Find the dimensions of the closed rectangular box with maximum volume that can be inscribed in the unit sphere.

Inessa [12570]

Answer:

Wyjaśnienie krok po kroku:

Załóżmy, że prostokąt ma wierzchołki (x,y,z) w dodatnim oktancie. Prostokątny pudełko musi być symetryczne względem wszystkich trzech osi.

Wtedy jego boki to

$2x,2y,2z$

Objętość = $8xyz$

Maksymalizuj objętość przy założeniu

$x^2+y^2+z^2 =1$

tj. $g(x,y,z) = x^2+y^2+z^2 -1=0$

Użyj mnożników Lagrange'a, mamy

$∇f(x,y,z)=λ∇g(x,y,z)$ przy maksimum

$∇f(x,y,z)=λ∇g(x,y,z) =(8yz,8xz,8xy)\\∇g(x,y,z)=(2x,2y,2z)$

$8yz=2λx8xz=2λy8xy=2λz$

Dzieląc otrzymujemy

$\frac{y}{x} =\frac{x}{y} \\x^2=y^2$

Podobnie $y^2=z^2$

Zatem otrzymujemy $3x^2 =1\\x = \frac{1}{\sqrt{3} }$

Stąd wymiary to

(2x,2y,2z)

$\frac{2}{\sqrt{3} },\frac{2}{\sqrt{3} },\frac{2}{\sqrt{3} } )$

</pzatem>

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zzz [12365]

28 might be an answer

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Which pair represents the same complex number?

tester [12383]

In this scenario, we have the complex number:
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