Question

Lim √1+x - √1-xx-0 ​

Answer 1

Ответ:

0

Пошаговое объяснение:

√1+0 - √1-0

Answer 2

To simplify the expression Lim √(1+x) - √(1-x)/(x-0), we can use some algebraic manipulation. The given expression seems to be the limit as x approaches 0.

Step 1: Combine the two square roots into a single fraction.

Lim [(√(1+x) - √(1-x)) / x] as x → 0

Step 2: Rationalize the numerator.

To rationalize the numerator, we can multiply the expression by its conjugate, which will eliminate the square root terms.

Lim [((√(1+x) - √(1-x)) / x) * ((√(1+x) + √(1-x)) / (√(1+x) + √(1-x)))] as x → 0

Step 3: Simplify the numerator.

The numerator simplifies due to the difference of squares:

Lim [(1+x) - (1-x) / x * (√(1+x) + √(1-x))] as x → 0

Step 4: Simplify the fraction.

Lim [(2x) / x * (√(1+x) + √(1-x))] as x → 0

Step 5: Cancel out x from the numerator and denominator.

Lim [2 * (√(1+x) + √(1-x))] as x → 0

Step 6: Substitute x = 0 into the expression.

Now, we can directly evaluate the expression as x approaches 0:

Lim [2 * (√(1+0) + √(1-0))] = Lim [2 * (1 + 1)] = Lim [4] = 4

Therefore, the simplified expression of Lim √(1+x) - √(1-x)/x as x approaches 0 is 4.