Question

What is the value of the limit as x approaches 1 of (x - 1) / (x * square root of -1)?

a) 0
b) [infinity]
c) i
d) 1

Answer 1

The value of the limit as x approaches 1 of (x - 1) / (x * square root of -1) is 0.

Step-by-step explanation:

In this case, we have the limit as x approaches 1 of (x - 1) / (x * square root of -1). To find the value of this limit, we can simplify the expression. The square root of -1 is represented by the imaginary unit i. So, the expression becomes (x - 1) / (x * i). Factorizing the expression, we get (x - 1) / (i * x). As x approaches 1, both x and i*x approach 1. Therefore, the limit becomes (1 - 1) / (i * 1) = 0 / i = 0. Hence, the value of the limit is 0.