None of the options can be multiplied by the fraction to determine the limit
How to determine the expression that evaluates the limit?
The function is given as:
lim x⇒ -1, (√(x - 1) -1)/(x + 1)
When x = -1
x + 1 becomes -1 + 1
This gives
x + 1 = 0
This means that the limit would approach infinity
When the denominator and the numerator are multiplied by x + 1, the denominator becomes
(x + 1)(x + 1)
Evaluate the product
x^2 + 2x + 1
When x = -1, we have:
(-1)^2 + 2(-1) + 1
This gives
0
This means that the limit would approach infinity
When the denominator and the numerator are multiplied by x - 1, the denominator becomes
(x - 1)(x + 1)
Evaluate the product
x^2 - 1
When x = -1, we have:
(-1)^2 - 1
This gives
0
This means that the limit would approach infinity
This is the same for the other options
Hence, none of the options can be multiplied by the fraction to determine the limit
Read more about function limits at:
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