MathDB

Problem 1

Part of 2014 VJIMC

Problems(2)

complex # equation (VJIMC 2014 1.1)

Source:

5/20/2021
Find all complex numbers zz such that ∣z3+2−2i∣+zz‾∣z∣=22.|z^3+2-2i|+z\overline z|z|=2\sqrt2.
complex numbersalgebra
limit(∞) of f(x)+f'(x)/x given, find lim(∞) f(x)

Source: VJIMC 2014 2.1

5/21/2021
Let f:(0,∞)→Rf:(0,\infty)\to\mathbb R be a differentiable function. Assume that lim⁡x→∞(f(x)+f′(x)x)=0.\lim_{x\to\infty}\left(f(x)+\frac{f'(x)}x\right)=0.Prove that lim⁡x→∞f(x)=0.\lim_{x\to\infty}f(x)=0.
limitlimitsreal analysis