Final answer:
To find the limit of (x - 4) / (√x - 2) as x approaches 4, multiply the expression by its conjugate to cancel out the (x - 4) term, which ultimately results in the answer being 4. Option c is the correct answer.
Step-by-step explanation:
The student has asked to find the limit as x approaches 4 of the expression (x - 4) / (√x - 2). To solve the mathematical problem completely, we need to address the fact that if we directly substitute x = 4 into the expression, we would get a 0/0 form which is undefined. This suggests that there is a common factor in the numerator and the denominator that we need to eliminate.
Let's factor by multiplying the numerator and the denominator by the conjugate of the denominator:
- Multiply by (√x + 2) / (√x + 2)
- This gives: ((x - 4)(√x + 2)) / ((√x - 2)(√x + 2))
- Simplify to get (x - 4) * (√x + 2) / (x - 4)
- Cancel out the (x - 4) terms.
- Now we have (√x+ 2)
We then directly substitute x = 4 and find the limit is 2 + 2, which is 4. Hence, the mention correct option answer in the final answer to the limit as x approaches 4 of (x - 4) / (√x - 2) is option C) 4.