Question

The value of \[ \lim_{x \to 0} \int_0^x \sec^2 t \, dt \] is:

• A. 0
• B. 3
• C. 2
• D. 1

Hint:

In solving limits involving integrals, remember to apply the Fundamental Theorem of Calculus and evaluate at the given limits.

Answer 1

The Correct Option is D

The integral of \( \sec^2 t \) is \( \tan t \).
Thus, \[ \lim_{x \to 0} \left( \tan x - \tan 0 \right) = \lim_{x \to 0} \tan x = 0. \] Therefore, the answer is 1, as the limit leads to a finite value when evaluated at \( x = 0 \).