Find the one-sided limit.
-$\lim _ { x \rightarrow \theta ^ { + } } ( 2 \cos x )$
A) -2
B) 2
C) 0
D) does not exist

Question

Quizplus · Accepted Answer

The one-sided limit of $2\cos x$ as $x$ approaches $\theta$ from the right is simply $2\cos(\theta)$, because the cosine function is continuous everywhere. Since $\cos(\theta)$ is defined for all real numbers and its maximum value is 1, $2\cos(\theta)$ will be 2 when $\theta$ is any angle where the cosine is 1 (e.g., $0$, $2\pi$, etc.). Therefore, without loss of generality, the limit is 2, assuming $\theta$ is such that $\cos(\theta) = 1$. However, even if $\theta$ is not specified, the question seems to imply evaluating the general behavior of $2\cos x$ as $x$ approaches any angle from the right, which would still be $2\cos(\theta)$, reflecting the continuous nature of the cosine function.

Find the One-Sided Limit lim⁡x→θ+(2cos⁡x)\lim _ { x \rightarrow \theta ^ { + } } ( 2 \cos x )limx→θ+​(2cosx)

Find the One-Sided Limit $\lim _ { x \rightarrow \theta ^ { + } } ( 2 \cos x )$