Learn how to solve limits to infinity problems step by step online. Find the limit of (1-cos(x))/(2-2e^(4x)) as x approaches 0. Factor the polynomial 2-2e^{4x} by it's greatest common factor (GCF): 2. The limit of the product of a function and a constant is equal to the limit of the function, times the constant. For example: \displaystyle\lim_{t\to 0}{\left(\frac{t}{2}\right)}=\lim_{t\to 0}{\left(\frac{1}{2}t\right)}=\frac{1}{2}\cdot\lim_{t\to 0}{\left(t\right)}. If we directly evaluate the limit \frac{1}{2}\lim_{x\to0}\left(\frac{1-\cos\left(x\right)}{1-e^{4x}}\right) as x tends to 0, we can see that it gives us an indeterminate form. We can solve this limit by applying L'Hôpital's rule, which consists of calculating the derivative of both the numerator and the denominator separately.

Find the limit of (1-cos(x))/(2-2e^(4x)) as x approaches 0