Question

Найти вертикальные асимптоты графика y=x^2/x^2-4 выполнить схематический чертеж

Answer 1

Найти вертикальные асимптоты графика y=x^2/x^2-4 выполнить схематический чертеж

Объяснение:

у=(х²):(х²-4)  .По определению знаменатель не должен быть равен нулю  х≠±2. Это точки разрыва.

В этих точках предел функции будет равен бесконечности, а это значит, что функция в этой точке бесконечно приближается к линии асимптоты.

lim  (х²):(х²-4) =4:(∞)=∞.

x → 2

lim  (х²):(х²-4) =4:(∞)=∞.

x → -2

Answer 2

Vertical Asymptotes of the Graph y = x^2/(x^2 - 4)

To find the vertical asymptotes of the graph of the function y = x^2/(x^2 - 4), we need to determine the values of x for which the denominator of the function becomes zero. Vertical asymptotes occur when the function approaches infinity or negative infinity as x approaches these values.

The denominator of the function is x^2 - 4. Setting it equal to zero and solving for x, we get:

x^2 - 4 = 0

Factoring the equation, we have:

(x - 2)(x + 2) = 0

This equation has two solutions: x = 2 and x = -2. Therefore, the vertical asymptotes of the graph occur at x = 2 and x = -2.

Schematic Diagram of the Graph

To create a schematic diagram of the graph y = x^2/(x^2 - 4), we can plot some key points and draw the shape of the graph based on its behavior.

1. Vertical Asymptotes: - Vertical asymptote at x = 2 - Vertical asymptote at x = -2

2. Key Points: - When x approaches positive infinity, y approaches 1. - When x approaches negative infinity, y approaches 1. - When x = 0, y = 0.

Based on these key points and the behavior of the function, we can sketch the schematic diagram of the graph as follows:

        |       /
        |      /
        |     /
        |    /
        |   /
        |  /
        | /
--------|-----------------
        |
        |
        |
        |
        |

Please note that this is a rough sketch and not an accurate representation of the graph. It is always recommended to use graphing software or a graphing calculator for a more precise visualization of the graph.

I hope this helps! Let me know if you have any further questions.