stefan-fürst-mathe-hü-2

2.21) a)

$$||"id":1076189461997||y=\frac{1}{x}\underset{x\to \infty }{\lim }\frac{1}{x}=0\underset{x\to -\infty }{\lim }\frac{1}{x}=0$$

b)

$$||"id":1368027710396||y=\frac{1}{x-2}\underset{x\to \infty }{\lim }\frac{1}{x-2}=0\underset{x\to -\infty }{\lim }\frac{1}{x-2}=0$$

g)

$$||"id":582868932643||y=\frac{6x^2-3}{2x^2+x+1}\underset{x\to \infty }{\lim }\frac{6x^2-3}{2x^2+x+1}=3\underset{x\to -\infty }{\lim }\frac{6x^2-3}{2x^2+x+1}=3$$

2.22 a)

$$||"id":1017300411637||y=\frac{x^2}{x-1}=1x^2:(x-1)=x-x^2-x0+xx+\frac{x^2}{x-1}=x+1$$

d) ich pack das nicht 2.23 a)

$$||"id":702177955070||\frac{\sqrt{x^2+1}}{x}=\frac{x+1}{x}\underset{x\to \infty }{\lim }\frac{x+1}{x}=1$$

b)

$$||"id":458273688883||\underset{x\to \infty }{\lim }\frac{3+2x}{1+2x}=1$$

2.25 a)

$$W=G\ast M\ast m(\frac{1}{r}-\frac{1}{r+h})||"id":166064668530||\underset{h\to \infty }{\lim }\frac{1}{r+h}=0G\ast M\ast m\ast \frac{1}{r}=10.25\ast 10^{7}J$$

b)

$$||"id":264661389779||W=G\ast M\ast m(\frac{1}{r}-\frac{1}{r+h})W_{\infty }=\frac{m\ast v^2}{2}=\frac{G\ast M\ast m}{r}v=\sqrt{\frac{2GM}{r}}\approx 40250kmh$$