Question

Lim cos4x = ?​

Answer 1

Объяснение:

$cos \frac{4}{1} \times - \frac{\pi}{2} = cos - 2\pi = - 1$

Answer 2

To find the value of $\lim_{{x \to 0}} \cos(4x)$, you can use the limit properties and trigonometric identities.

Recall the trigonometric identity: $\cos(2\theta) = 1 - 2\sin^2(\theta)$

Now, let's use this identity with $\theta = 2x$: $\cos(4x) = 1 - 2\sin^2(2x)$

Now, take the limit as $x$ approaches 0: $\lim_{{x \to 0}} \cos(4x) = \lim_{{x \to 0}} \left(1 - 2\sin^2(2x)\right)$

Now, we can apply the limit properties. The limit of a sum or difference is the sum or difference of the limits, and the limit of a constant is the constant itself. Additionally, the limit of sine squared as $x$ approaches 0 is 0 because $\sin(0) = 0$. Therefore, the limit simplifies to:

$\lim_{{x \to 0}} \cos(4x) = 1 - 2 \cdot 0 = 1$

So, $\lim_{{x \to 0}} \cos(4x) = 1$.