Given:
f(x) = |x| − 5
Step 1: Analyze the function near x = 5
Since 5 is a positive number,
|x| = x (for x near 5)
So, f(x) = x − 5
Step 2: Evaluate the limit
limx→5 f(x) = limx→5 (x − 5)
= 5 − 5
= 0
Final Answer:
limx→5 f(x) = 0
The area of the region \( \{(x, y): 0 \leq y \leq x^2 + 1, \, 0 \leq y \leq x + 1, \, 0 \leq x \leq 2\ \) is:}