Does $$\lim_{x \to – \infty} \left(\frac{\pi}{2} + \arctan{x} \right) \cdot x = – \infty$$?
My logic is that “something“ times "negative infinity" equals negative infinity. Am I right?
calculusinfinitylimits
Does $$\lim_{x \to – \infty} \left(\frac{\pi}{2} + \arctan{x} \right) \cdot x = – \infty$$?
My logic is that “something“ times "negative infinity" equals negative infinity. Am I right?
Best Answer
The sentence "something times negative infinity equals negative infinity" is wrong in more than one way:
The limit you must calculate is a limit of a product of two numbers, one tends to $0$, the other to $-\infty$. Such a limit is often best approached using L'Hospital's rules.