Given:
limx→0 x · sec x
Step 1: Rewrite sec x
sec x = 1 / cos x
Step 2: Apply limits
As x → 0,
x → 0
cos x → 1
Step 3: Evaluate the limit
limx→0 x · sec x = 0 × 1
= 0
Final Answer:
limx→0 x · sec 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:}