Question

Lim(x→-1)=x+1/√x+5-√3-x

Answer 1

Ответ:

Пошаговое объяснение:

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Answer 2

To find the limit of the given expression as x approaches -1, we need to evaluate the expression when x is very close to -1.

Let's work on it step by step:

1. Substitute x = -1 into the expression: lim(x→-1) [(x + 1) / (√x + 5 - √3 - x)]

   Plugging in x = -1: = (-1 + 1) / (√(-1) + 5 - √3 - (-1)) = 0 / (√(-1) + 5 + 1) = 0 / (√(-1) + 6)

2. Now, let's simplify the denominator: Since √(-1) is the square root of a negative number, it is not a real number. However, it can be represented using the imaginary unit 'i' as √(-1) = i.

   So the expression becomes: = 0 / (i + 6)

3. To remove the denominator's complex number (i + 6), we can multiply both the numerator and denominator by the complex conjugate of (i + 6), which is (i - 6):

   = (0 / (i + 6)) * ((i - 6) / (i - 6)) = 0 * (i - 6) / ((i + 6) * (i - 6)) = 0 / (i^2 - 6i + 6i - 36) = 0 / (i^2 - 36)

4. Recall that i^2 is defined as -1: = 0 / (-1 - 36) = 0 / (-37)

5. Any number divided by zero is undefined. Therefore, the limit of the given expression as x approaches -1 is undefined.

In summary, the limit lim(x→-1) [(x + 1) / (√x + 5 - √3 - x)] is undefined.