Find the limit.
-$\lim _ { t \rightarrow 0 } \sec \left( \frac { - 2 \pi t } { \sin t } \right)$
A) 1
B) $- 1$
C) $- \frac { 1 } { 2 }$
D) 0

Question

Quizplus · Accepted Answer

We can use the fact that $\sin t$ is approximately equal to $t$ for small values of $t$ to simplify the expression inside the secant:
\begin{align*}
\frac{-2\pi t}{\sin t} &= \frac{-2\pi}{\frac{\sin t}{t}}\
&\approx \frac{-2\pi}{1}\
&= -2\pi.
\end{align*}
So as $t$ approaches $0$, the expression inside the secant approaches $-2\pi$, and $\sec(-2\pi)$ is equal to $1$. Therefore, the limit is $\boxed{	ext{(A) }1}$.

Find the Limit lim⁡t→0sec⁡(−2πtsin⁡t)\lim _ { t \rightarrow 0 } \sec \left( \frac { - 2 \pi t } { \sin t } \right)limt→0​sec(sint−2πt​)

Find the Limit $\lim _ { t \rightarrow 0 } \sec \left( \frac { - 2 \pi t } { \sin t } \right)$